GATE Overflow - Recent questions in Combinatory
http://gateoverflow.in/questions/mathematics/discrete-mathematics/combinatory
Powered by Question2Answerrosen example 20
http://gateoverflow.in/144877/rosen-example-20
how many different ways are there to seat 4 people around a circular table ,where two sittings are considered the same when each person has same left and right neighbour?Combinatoryhttp://gateoverflow.in/144877/rosen-example-20Thu, 17 Aug 2017 09:06:46 +0000UPSC prelim test
http://gateoverflow.in/144083/upsc-prelim-test
<p><strong>A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag </strong><strong>blind-folded</strong><strong> (without replacing any of it) to be assured of picking </strong><strong>atleast</strong><strong> one ball of each </strong><strong>colour</strong><strong>?</strong></p>
<p>a) 15 </p>
<p>b) 16</p>
<p>c) 17</p>
<p>d)18</p>Combinatoryhttp://gateoverflow.in/144083/upsc-prelim-testMon, 14 Aug 2017 11:16:58 +0000#combinotirics
http://gateoverflow.in/143639/%23combinotirics
Find the largest integer value of x such that the following inequality holds:<br />
<br />
(10 C x-1) <2*(10 C x)<br />
<br />
In this question if solved line by line i am getting x<6.<br />
<br />
but clearly if you put x=7, it satisfies the inequality and 7 becomes the largest integer. <br />
<br />
Is there a procedure to get answer 7 step by step??Combinatoryhttp://gateoverflow.in/143639/%23combinotiricsSat, 12 Aug 2017 17:39:46 +0000counting
http://gateoverflow.in/143079/counting
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=13048640937689002281"></p>
<p>what does it mean that "each person has same left and right neighbour "?</p>Combinatoryhttp://gateoverflow.in/143079/countingThu, 10 Aug 2017 16:53:03 +0000General Combinatorics
http://gateoverflow.in/142942/general-combinatorics
<h1>How many 6 digit numbers can be formed from 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6?</h1>Combinatoryhttp://gateoverflow.in/142942/general-combinatoricsThu, 10 Aug 2017 07:34:30 +0000Sheldon Ross - Probability (2nd chapter)
http://gateoverflow.in/141823/sheldon-ross-probability-2nd-chapter
<p>Poker dice is played by simultaneously rolling 5 dice.Show that</p>
<p>(a) P{no two alike} = .0926;
<br>
(b) P{one pair} = .4630;
<br>
(c) P{two pair} = .2315;
<br>
(d) P{three alike} = .1543;
<br>
(e) P{full house} = .0386;
<br>
(f) P{four alike} = .0193;
<br>
(g) P{five alike} = .0008.</p>
<p><span class="marker">My doubt is how is this different from poker played by cards? Is it that when we play via dice the order of the dice outcome matters which doesn't in case of cards.(i.e the order of cards in hand). So if we think the case of having one pair as </span></p>
<p><span class="marker"><6 6 5 1 2> and <6 5 1 2 6> both outcomes are different?</span></p>
<p><span class="marker">but <6(1st six) 5 1 2 6 (second six)> and <6(2nd six) 5 1 2 6(1st six)> both are same,since its the same one pair but the pairs doesn't generate new outcome when position is changed.</span></p>
<p>i.e for question (b) probability is = 6C1 (for selecting pair outcome) * 5C2 (possibility of selecting a pair of hand out of five,but order does not matter when pair partners are exchanged) * 5 * 4* 3 (because order matters of the outcomes of other non-pairs) this total divided by 6^5. Is my assumption true?</p>Combinatoryhttp://gateoverflow.in/141823/sheldon-ross-probability-2nd-chapterSat, 05 Aug 2017 07:41:33 +0000Seldon Ross
http://gateoverflow.in/140617/seldon-ross
A president,treasurer and secretary,all different,are to be chosen from a club consisting of 10 people.How many different choices of officers are possible if<br />
<br />
a)A and B will not serve together<br />
<br />
b)C and D serve together or not at all?<br />
<br />
c)E must be an officer?<br />
<br />
d)F will serve only if he is present?Combinatoryhttp://gateoverflow.in/140617/seldon-rossSun, 30 Jul 2017 05:42:57 +0000Seldon Ross
http://gateoverflow.in/140615/seldon-ross
How many 5 digit numbers can be formed from the integers 1,2......9 if no digit can appear more than twice?Combinatoryhttp://gateoverflow.in/140615/seldon-rossSun, 30 Jul 2017 05:38:36 +0000combinatory
http://gateoverflow.in/140181/combinatory
let S be the set of natural numbers whose digits are chosen from {1,3,5,7} such that no digits are repeated find<br />
<br />
1) |S|<br />
<br />
2) $\sum (n)$ where n belongs to s<br />
<br />
first part i know 64 numbers would be there how to approach 2nd partCombinatoryhttp://gateoverflow.in/140181/combinatoryThu, 27 Jul 2017 08:49:54 +0000combinatory
http://gateoverflow.in/140179/combinatory
how many ways are there to seat n married couples(n>=3) around a table such that men and women alternate and each women is not adjacent to her husband?Combinatoryhttp://gateoverflow.in/140179/combinatoryThu, 27 Jul 2017 08:41:29 +0000#gate
http://gateoverflow.in/139847/%23gate
Any good resource on Generating function and recurrrence relations ?Combinatoryhttp://gateoverflow.in/139847/%23gateTue, 25 Jul 2017 16:38:41 +0000Is Summation topic in GATE syllabus
http://gateoverflow.in/139406/is-summation-topic-in-gate-syllabus
Is summation is in Gate 2018 syllabus?Combinatoryhttp://gateoverflow.in/139406/is-summation-topic-in-gate-syllabusSun, 23 Jul 2017 13:37:51 +0000Combination (Repetition)
http://gateoverflow.in/139141/combination-repetition
A girl has to choose 4 items from a bucket which contains 3 red, 3 green, and 4 blue balls, now in how many ways she can do this?Combinatoryhttp://gateoverflow.in/139141/combination-repetitionSat, 22 Jul 2017 06:00:19 +0000Combination(Repetition) followed by Permutation(Repetition)
http://gateoverflow.in/139117/combination-repetition-followed-permutation-repetition
<p>No of balls = 3 identical red, 3 identical blue, 4 identical green.</p>
<p>Urns = U1, U2, U3.</p>
<p>Now my doubt here is that we can arrange all these 10 balls in those 3 urns as C(10+3-1, 3-1) or C(10+3-1,10), but consider a urn which has content as <strong>2 red balls and 2 green balls. </strong></p>
<p>which can be arranged in:-</p>
<p>fact(4)/ { fact(2) * fact(2) } = 6</p>
<p>but in through this formula:-</p>
<p>C(10+3-1, 3-1) </p>
<p>we are calculating 6 different permutations as 1 in that urn. And similar happening with other urns also.</p>
<p>So, how we can resolve such kind of question?</p>Combinatoryhttp://gateoverflow.in/139117/combination-repetition-followed-permutation-repetitionSat, 22 Jul 2017 04:26:07 +0000Permutations
http://gateoverflow.in/138743/permutations
How many different words of 3 length can be formed from a,e,i,o,u containing a,e ?Combinatoryhttp://gateoverflow.in/138743/permutationsWed, 19 Jul 2017 16:28:09 +0000Discreate Random Variable (Rose_8th Edition)
http://gateoverflow.in/138439/discreate-random-variable-rose_8th-edition
Three balls are to be randomly selected without replacement from an urn containing 20 balls numbered 1 through 20. If we bet that at least one of the balls that are drawn has a number as large as or larger than 17, what is the probability that we win the bet?<br />
<br />
My Approach through random variables:<br />
<br />
let X is the random variable defined as:<br />
<br />
X = number of balls having the number on them >= 17 in three drawn.<br />
<br />
In the question, they have asked for at least 1 then we can place the values of X are 1,2,3;<br />
<br />
P(X = 1 ) = (4/20) * (16/19) * (15 / 18) = 0.14035<br />
<br />
P(X = 2 ) = (4/20) * (3/19) * (16 / 18) = 0.02807<br />
<br />
P(X = 3 ) = (4/20) * (3/19) * (2 / 18) = 0.00350<br />
<br />
Prob of wining bet = P(X=1) + P(X=2) + P(X=3) <br />
<br />
= 0.17192<br />
<br />
but the answer is 0.508<br />
<br />
what is wrong with this approach.Combinatoryhttp://gateoverflow.in/138439/discreate-random-variable-rose_8th-editionTue, 18 Jul 2017 05:33:06 +0000Generating Function Question
http://gateoverflow.in/138235/generating-function-question
<p>I got (x^20).1/(1+x).1/(1-x)^3 .
<br>
Now, if I write this as -
<br>
[x^20].(1+x)^-1.(1-x)^-3</p>
<p>Now, I don't know how to solve this further when we have both factors having negative n.</p>
<p> </p>
<p>Please don't send me here - <a rel="nofollow" href="http://gateoverflow.in/65803/find-number-integral-solutions-using-generating-function">http://gateoverflow.in/65803/find-number-integral-solutions-using-generating-function</a> </p>
<p>As i Didn't get that solution.</p>
<p> </p>
<p>Someone please simplify it.</p>Combinatoryhttp://gateoverflow.in/138235/generating-function-questionSun, 16 Jul 2017 16:32:02 +0000How to find this coefficient in this question?
http://gateoverflow.in/137957/how-to-find-this-coefficient-in-this-question
Find coeff of x^83 in [x^83].(x^5+x^8+x^11+x^14+x^17)Combinatoryhttp://gateoverflow.in/137957/how-to-find-this-coefficient-in-this-questionSat, 15 Jul 2017 08:12:49 +0000Question on Number System
http://gateoverflow.in/137519/question-on-number-system
Find the remainder of $\frac{9^{1}+9^{2}+...+9^{n}}{6}$ where $n$ is multiple of 11.<br />
<br />
I am getting $0$ or $3$. But given answer is 3. Can anyone check?Combinatoryhttp://gateoverflow.in/137519/question-on-number-systemThu, 13 Jul 2017 04:32:00 +0000Question on Number System.
http://gateoverflow.in/137518/question-on-number-system
If $N = 1!+2!+3!+...+10!$. What is the last digit of $N^{N}$?Combinatoryhttp://gateoverflow.in/137518/question-on-number-systemThu, 13 Jul 2017 04:07:20 +0000rosen #section 5.5 question 15(d) page no 378
http://gateoverflow.in/137453/rosen-%23section-5-5-question-15-d-page-no-378
Combinatoryhttp://gateoverflow.in/137453/rosen-%23section-5-5-question-15-d-page-no-378Wed, 12 Jul 2017 13:59:53 +0000rosen Exer:5.5 15(c) how many solutions are there for x1+x2+x3+x4+x5=21 such that 0<=x1<=10?(detailed explanation)
http://gateoverflow.in/137443/rosen-exer-many-solutions-there-that-detailed-explanation
Combinatoryhttp://gateoverflow.in/137443/rosen-exer-many-solutions-there-that-detailed-explanationWed, 12 Jul 2017 13:04:02 +0000rosen exercise problem
http://gateoverflow.in/137257/rosen-exercise-problem
<p><strong>How many bit strings of length 10 contain at least three 1s and at least three 0s?</strong></p>
<p><strong>My Approach:-></strong></p>
<p><strong>using product rule</strong></p>
<p><strong> There are 3 subtask following</strong></p>
<p><strong><img alt="T_{1}" src="http://latex.codecogs.com/gif.latex?T_%7B1%7D"> (filling 3 ones in 10 places) =<img alt="\binom{10}{3}" src="http://latex.codecogs.com/gif.latex?%5Cbinom%7B10%7D%7B3%7D"></strong></p>
<p><strong><img alt="T_{2}" src="http://latex.codecogs.com/gif.latex?T_%7B2%7D"> (filling 3 zeros in remaing 7 places) =<img alt="\binom{7}{3}" src="http://latex.codecogs.com/gif.latex?%5Cbinom%7B7%7D%7B3%7D"></strong></p>
<p><img alt="T_{3}" src="http://latex.codecogs.com/gif.latex?T_%7B3%7D"> <strong>(filling remaining 4 places) =</strong> <img alt="2^{4}" src="http://latex.codecogs.com/gif.latex?2%5E%7B4%7D"></p>
<p><strong>So,total number of bit string = <img alt="\binom{10}{3}" src="http://latex.codecogs.com/gif.latex?%5Cbinom%7B10%7D%7B3%7D">*<img alt="\binom{7}{3}" src="http://latex.codecogs.com/gif.latex?%5Cbinom%7B7%7D%7B3%7D">*<img alt="2^{4}" src="http://latex.codecogs.com/gif.latex?2%5E%7B4%7D"> which is greater than <img alt="2^{10}" src="http://latex.codecogs.com/gif.latex?2%5E%7B10%7D">(total number of string).</strong></p>
<p><strong>Now , i want to know what is wrong in my apporach. please explain..</strong></p>Combinatoryhttp://gateoverflow.in/137257/rosen-exercise-problemTue, 11 Jul 2017 12:01:02 +0000Kenneth Rosen Counting 6.5 Example 6
http://gateoverflow.in/137164/kenneth-rosen-counting-6-5-example-6
<p>What is the value of k after the following pseudocode has been executed?</p>
<pre class="prettyprint">
k := 0
for i1 := 1 to n
for i2 := 1 to i1
·
·
·
for im := 1 to im−1
k := k + 1
</pre>
<p>The solution given is:
<br>
$k = C(n + m − 1,m)$</p>
<p>(A) C(n + m – 1, m)
<br>
(B) C(n – m + 1, m)
<br>
(C) C(n + m – 1, n)
<br>
(D) C(n – m + 1, n) </p>
<p>How do we reach this answer?
<br>
I'm not getting why they used the r-permutation formula here.</p>Combinatoryhttp://gateoverflow.in/137164/kenneth-rosen-counting-6-5-example-6Tue, 11 Jul 2017 03:01:09 +0000gatebook
http://gateoverflow.in/136871/gatebook
How many bit strings of length $6$ have more no of zeros than ones??<br />
<br />
We can solve this drawing tree but it takes so much time Is there any other way??Combinatoryhttp://gateoverflow.in/136871/gatebookSun, 09 Jul 2017 08:47:05 +0000GATEbook
http://gateoverflow.in/136859/gatebook
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7509052260239437586"></p>Combinatoryhttp://gateoverflow.in/136859/gatebookSun, 09 Jul 2017 07:20:17 +0000Gatebook
http://gateoverflow.in/136829/gatebook
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11790649760514761116"></p>
<p> </p>
<p>I am not able to understand the last component in square brackets we have to minus from all combinations the combinations with that dotted line but intersection part i didn't get</p>Combinatoryhttp://gateoverflow.in/136829/gatebookSun, 09 Jul 2017 02:46:56 +0000Rosen Counting Permutations
http://gateoverflow.in/136682/rosen-counting-permutations
I was doing two Questions of rosen counting chapter<br />
<br />
Q1. A group contains n mens and n women. How many ways are there to "arrange" these people in a row if the men and women alternate ?<br />
<br />
Answer is 2(n!)^2, I agree with logic and answer.<br />
<br />
<br />
<br />
Q2. How many ways are there for eight men and five women to stand in a line so that no two women stand next to each other?<br />
<br />
Answer is P(8,8)*P(9,5), I also agree with answer and logic.<br />
<br />
<br />
<br />
My dobut is, The frame of questions are similar but then why can't we solve Q1 with the approach used in Q2 i.e. first permuting n men and then choosing n women places from (n+1) places created my positioning the men and permuting them again i.e P(n,n)*P(n+1,n) ??Combinatoryhttp://gateoverflow.in/136682/rosen-counting-permutationsSat, 08 Jul 2017 07:32:52 +0000Discrete Mathematics for Computer Scientists and Mathematicians , Chapter- 2 , Exercise- 2.2, Question-4
http://gateoverflow.in/135877/discrete-mathematics-computer-scientists-mathematicians
<p>1- Determine the number of 5-combinations of { 1.a , ∞.b ,∞.c , 1.d }. </p>
<p>2<strong>-More generally , develop a formula for the number of r-combinations of a collection of letters a<sub>1 , </sub>a<sub>2 </sub>, ..., a<sub>k </sub>whose repetition numbers are either 1 or ∞.</strong></p>
<p>P.S. i got the answer of 1st but unable to generalize it as asked in 2nd.</p>Combinatoryhttp://gateoverflow.in/135877/discrete-mathematics-computer-scientists-mathematiciansMon, 03 Jul 2017 14:55:09 +0000Discrete Mathematics for Computer Scientists and Mathematicians , Chapter- 2 , Exercise- 2.1, Question-36
http://gateoverflow.in/135833/discrete-mathematics-computer-scientists-mathematicians
Twenty athletes compete in a contest. Each of 3 judges assign 20 different ratings to the 20 athletes. For an athlete to be named winner he must be given the highest rating by at least 2 judges. Compute the fraction of cases for which a winner is named.Combinatoryhttp://gateoverflow.in/135833/discrete-mathematics-computer-scientists-mathematiciansMon, 03 Jul 2017 07:59:32 +0000Equal coefficients
http://gateoverflow.in/135519/equal-coefficients
$\begin{align*} &A = \left ( p x + q \right )^{504} \text{ where p and q are +ve integers and }gcd(p,q) = 1 \\ &\text{Given } \left [ x^4 \right ] = \left [ x^5 \right ] , \text{ where } \left [ x^k \right ] \text{ denote the coefficient of }x^k \text{ in A.} \\ &\text{What is p+q ?} \end{align*}$Combinatoryhttp://gateoverflow.in/135519/equal-coefficientsSat, 01 Jul 2017 04:54:42 +0000Sheldon Ross Chapter 1 Example 3c
http://gateoverflow.in/134909/sheldon-ross-chapter-1-example-3c
Ms. Jones has 10 books that she is going to put on her bookshelf. Of these, 4 are mathematics books, 3 are chemistry books, 2 are history books, and 1 is a language book. Ms. Jones wants to arrange her books so that all the books dealing with the same subject are together on the shelf. How many different arrangements are possible? <br />
<br />
Please provide a different explanation rather than the textbook one.Combinatoryhttp://gateoverflow.in/134909/sheldon-ross-chapter-1-example-3cTue, 27 Jun 2017 06:52:14 +0000combinatorial argument
http://gateoverflow.in/134885/combinatorial-argument
$\begin{align*} &\text{Prove using combinatorial argument } \\ &1) \qquad \text{For } n \geq k \geq 0 \qquad \left ( n-k \right )\cdot \binom{n}{k} = n \cdot \binom{n-1}{k} \\ &2) \qquad \text{For } n \geq 2 \qquad \quad k \cdot (k-1) \cdot \binom{n}{k} = n \cdot (n-1) \cdot \binom{n-2}{k-2} \\ \end{align*}$Combinatoryhttp://gateoverflow.in/134885/combinatorial-argumentTue, 27 Jun 2017 04:05:50 +0000Integer Sequence
http://gateoverflow.in/134882/integer-sequence
$\begin{align*} &\text{A} = \text{Set of integer sequence }\left ( a_1,a_2,a_2 ,\dots , a_k \right ) \\ &\text{where } 1 \leq a_1 \leq a_2 \leq a_3 \leq \dots \leq a_k \leq n \\ &\text{B} = \text{Set of integer sequence }\left ( b_1,b_2,b_2 ,\dots , b_k \right ) \\ &\text{where } 1 \leq b_1 < b_2 < b_3 < \dots < b_k \leq n \\ \end{align*}$<br />
<br />
Prove that $\begin{align*} |A| = |B| \end{align*}$Combinatoryhttp://gateoverflow.in/134882/integer-sequenceTue, 27 Jun 2017 03:38:12 +0000Combinatoric properties
http://gateoverflow.in/134880/combinatoric-properties
Prove that :<br />
$\begin{align*} &\text{For n , k , m are integers and } 0 < m \leq k < n \\ &\text{GCD}\left [ \binom{n}{m},\binom{n}{k} \right ] > 1 \\ \end{align*}$Combinatoryhttp://gateoverflow.in/134880/combinatoric-propertiesTue, 27 Jun 2017 03:13:43 +0000Combinatory
http://gateoverflow.in/134611/combinatory
How many ordered quadruples $\left ( x_{1},x_{2},x_{3},x_{4} \right )$ of odd positive integers satisfy<br />
<br />
$$x_{1}+x_{2}+x_{3}+x_{4}=98?$$Combinatoryhttp://gateoverflow.in/134611/combinatorySat, 24 Jun 2017 13:41:31 +0000Recurrence Relation
http://gateoverflow.in/134583/recurrence-relation
<p>The solution of <strong>a<sub>n</sub> = 2a<sub>n-1</sub><sub> </sub>+ 1</strong> where <strong>a<sub>0 </sub>= 1</strong> is ? </p>
<p>Please use the <strong>substitution method</strong> because I seem to have problem understanding it.</p>Combinatoryhttp://gateoverflow.in/134583/recurrence-relationSat, 24 Jun 2017 07:51:08 +0000Combinatorics : Multinomial Coefficients
http://gateoverflow.in/134546/combinatorics-multinomial-coefficients
<p>What's the relationship between combination and polynomial equation? I mean, I am not able to grasp certain points here or let's say connect them into a whole:
<br>
<br>
1. Take a question where it's asked that we have to arrange 10 books : 4 of A, 3 of B, 2 of C, and 1 of D in such a way that each book of similar type remain with its own type so like AAAABBBDCCC, etc. Here we are doing 4!*4!*3!*2!*1!.
<br>
<br>
2. When we take a question of dividing 10 police officers into 3 groups: 10 -> 5,3,2. Here we use 10!/*5!*3!*2!).
<br>
<br>
3. How many solutions of $x1+x2+x3+...+xn=300$ are possible?
<br>
<br>
Doubt: What's the difference between 1 & 2? Isn't two equivalent to saying arrange 10 officers like manner of AAAAABBBCC? If we are grouping 10 distinct elements into 3 groups where each group is of same type, then what's the catch here?
<br>
<br>
Second is what's the similarity between 2 and 3? Isn't three equivalent to saying group 300 distinct element into 3 bags/groups?
<br>
<br>
I am totally confuse here and I think I cannot move ahead with my GATE preparation if I cannot clear my doubt on combinatorics which in turn would mean no way of doing probability's tricky questions.</p>
<p> </p>
<p>EDIT: Here's the images of different questions. How do I differentiate between them?</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9083059680419989013"><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=14165371670004274780"></p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11854156684812671111"></p>Combinatoryhttp://gateoverflow.in/134546/combinatorics-multinomial-coefficientsSat, 24 Jun 2017 01:58:38 +0000Derangements
http://gateoverflow.in/134403/derangements
How many ways we can put 5 letters L1, L2, L3, L4, L5 in 5 envelopes e1, e2, e3, e4 and e5 (at 1 letter per envelope) so that<br />
<br />
i. no letter is correctly placed?<br />
<br />
ii. at least 1 letter is correctly placed?<br />
<br />
iii. exactly 2 letters are correctly placed?<br />
<br />
iv. at most 1 letter is correctly placed?<br />
<br />
v. at least 1 letter is wrongly placed?<br />
<br />
vi. exactly 1 letter is wrongly placed?Combinatoryhttp://gateoverflow.in/134403/derangementsFri, 23 Jun 2017 03:31:20 +0000#combinatory
http://gateoverflow.in/133790/%23combinatory
<p><strong>Determine the number of factors of 3<sup>4</sup> * 5<sup>2</sup> * * 11<sup>7</sup> * 13<sup>8</sup>.</strong></p>Combinatoryhttp://gateoverflow.in/133790/%23combinatoryMon, 19 Jun 2017 05:32:07 +0000#Discrete #Combinatorics
http://gateoverflow.in/132665/%23discrete-%23combinatorics
The number of ways in which n distinct objects can be put into two identical boxes so that no box remains empty, is<br />
<br />
a) 2^n - 1<br />
<br />
b) 2^n - 2<br />
<br />
c) 2^(n-1) - 1<br />
<br />
d) None of these<br />
<br />
Please explain your answer.Combinatoryhttp://gateoverflow.in/132665/%23discrete-%23combinatoricsSun, 11 Jun 2017 12:33:15 +0000[Discrete Maths] Counting ,Number of solutions to the equation
http://gateoverflow.in/132586/discrete-maths-counting-number-of-solutions-to-the-equation
How many solutions are there to the equation<br />
x1 + x2 + x3 + x4 + x5 = 21,<br />
where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that:<br />
<br />
0 ≤ x1 ≤ 3 , 1 ≤ x2 < 4 and 15≤x3 ?Combinatoryhttp://gateoverflow.in/132586/discrete-maths-counting-number-of-solutions-to-the-equationSat, 10 Jun 2017 17:55:46 +0000recurrence relation (rosen )
http://gateoverflow.in/131797/recurrence-relation-rosen
<p>solve the given recurrence relation ?</p>
<p> </p>
<hr>
<hr>
<p>$a_{n}=3a_{n/2}+n$</p>
<p>n=2^k , $a_{1}$=1</p>
<p>by changing the variables $b_{k}=3b_{k-1}+2^{k}$</p>
<p>after solving this i got c1.$3^{k}-2.2^{k}$</p>
<p>now i am facing difficulty to find the value of c1 ... might be silly can some one help me </p>Combinatoryhttp://gateoverflow.in/131797/recurrence-relation-rosenSun, 04 Jun 2017 06:56:22 +0000Generating function , closed form
http://gateoverflow.in/131674/generating-function-closed-form
Find a closed form for the generating function for the given sequence<br />
<br />
1) 1,1,0,1,1,1,1,1.....<br />
<br />
2) 1,2,1,1,1,1,1.....<br />
<br />
Do manually ..Combinatoryhttp://gateoverflow.in/131674/generating-function-closed-formSat, 03 Jun 2017 01:53:33 +0000Rosen example ( generating function)
http://gateoverflow.in/131673/rosen-example-generating-function
Let the alphabet consist of {0,1,2} find the number of r digit binary sequence that contain an even number of 0's.Combinatoryhttp://gateoverflow.in/131673/rosen-example-generating-functionSat, 03 Jun 2017 01:03:44 +0000Generalised permutation and combination
http://gateoverflow.in/131559/generalised-permutation-and-combination
Suppose that a basketball league has 32 teams ,split into 2 conference of 16 teams each . Each conference is splits into 3 division .suppose that north central Division plays 4 games against each of other teams in this division , 3 games against each of the 11 remaining teams in the conference , and 2 games against each of the 16 teams in the other conference ,in how many different order can the games of one of the teams in the north central Division scheduled ? <br />
<br />
I am unable to approach , little bit confusion in question statement ... please reply in detail ..Combinatoryhttp://gateoverflow.in/131559/generalised-permutation-and-combinationFri, 02 Jun 2017 03:52:56 +0000Permutation
http://gateoverflow.in/131551/permutation
How many strings with 5 or more characters can be formed from the letter SEERESS ? <br />
<br />
Verify the answer ...Combinatoryhttp://gateoverflow.in/131551/permutationFri, 02 Jun 2017 00:53:40 +0000Kenneth rosen exercise 6.3 Q.29
http://gateoverflow.in/131467/kenneth-rosen-exercise-6-3-q-29
How many 4-permutations of the positive integers not exceeding 100 contain three consecutive integers k,k+1,k+2, in the correct order<br />
<br />
A.) Where these consecutive integers can perhaps be separated by other integerd in the permutation ?<br />
<br />
B.) Whre they are in consecutive positions in the permutation ?Combinatoryhttp://gateoverflow.in/131467/kenneth-rosen-exercise-6-3-q-29Thu, 01 Jun 2017 11:30:00 +0000Cominatroics
http://gateoverflow.in/131345/cominatroics
There are 12 copies of Mathematics, 7 copies of Engineering, 3 different books on Medicine and 2 different books on Economics. Find the number of ways in which one or more than one book can be selected?<br />
A. 3421 B. 3111<br />
C. 3327 D. 3201Combinatoryhttp://gateoverflow.in/131345/cominatroicsWed, 31 May 2017 06:23:35 +0000#combinatroics
http://gateoverflow.in/131310/%23combinatroics
An elevator starts at the basement with 8 people (not including the elevator operator) and discharges them all by the time it reaches the top floor, number 6. In how many ways could the operator have perceived the people leaving the elevator if all people look alike to him? What if the 8<br />
people consisted of 5 men and 3 women and the operator could tell a man from a woman?Combinatoryhttp://gateoverflow.in/131310/%23combinatroicsTue, 30 May 2017 13:45:41 +0000