GATE Overflow - Recent questions in Combinatory
https://gateoverflow.in/questions/mathematics/discrete-mathematics/combinatory
Powered by Question2AnswerP and C doubt
https://gateoverflow.in/159677/p-and-c-doubt
Given a 4 *4 grid points , how many Triangles with vertices on the grid can be formed?Combinatoryhttps://gateoverflow.in/159677/p-and-c-doubtFri, 13 Oct 2017 09:29:12 +0000P and C doubt
https://gateoverflow.in/159661/p-and-c-doubt
Number of ways in which the corner of the square can coloured with two colours.<br />
<br />
It is permissible to use single colour on all four corners?Combinatoryhttps://gateoverflow.in/159661/p-and-c-doubtFri, 13 Oct 2017 08:12:06 +0000P and C doubt
https://gateoverflow.in/159639/p-and-c-doubt
In how many ways can 10 different books be distributed to three students A B C so that student A receives at least one book?<br />
<br />
<br />
<br />
In how many ways can 10 different books be distributed to three students ?<br />
<br />
<br />
<br />
In how many ways can 10 different books be distributed to three students A B C so that each student receives at least 3 books?<br />
<br />
How to solve these types of questions...<br />
<br />
Any type of assistance would be appreciated..Combinatoryhttps://gateoverflow.in/159639/p-and-c-doubtFri, 13 Oct 2017 07:06:52 +0000boys and 4 girls have to sit in a row with all arrangements equally likely
https://gateoverflow.in/159364/boys-and-girls-have-sit-row-with-arrangements-equally-likely
3 boys and 4 girls have to sit in a row with all arrangements equally likely. What is the probability that no 2 boys sit next to each other<br />
<br />
a)1/7 b)2/7 c) 3/7 d)4/7Combinatoryhttps://gateoverflow.in/159364/boys-and-girls-have-sit-row-with-arrangements-equally-likelyThu, 12 Oct 2017 05:20:18 +0000K. Rosen: Countings
https://gateoverflow.in/159361/k-rosen-countings
<p><strong>Question</strong> How many different strings of length 2 can be made from the letters in '<strong>ORONO</strong>'?</p>
<p>I am getting 7 strings as follows: OO, ON, OR, NO, RO, RN, NR
<br>
but given<strong> answer is 6</strong>.</p>
<p> </p>Combinatoryhttps://gateoverflow.in/159361/k-rosen-countingsThu, 12 Oct 2017 05:16:46 +0000P & C doubt
https://gateoverflow.in/159265/p-%26-c-doubt
In how many Ways can 5 numbers be selected and arranged in ascending order from set 1 2 3 4 5 6 7 8 9 10?<br />
<br />
Ans. Is it 10C5 * 1ways<br />
<br />
Please correct me if I m wrong..Combinatoryhttps://gateoverflow.in/159265/p-%26-c-doubtWed, 11 Oct 2017 15:29:45 +0000P and C doubt
https://gateoverflow.in/159137/p-and-c-doubt
How many number must be chosen from site {1 2 3 4 5 6 7 8 }such that at least two of them must have sum equal to 9?<br />
<br />
A.28<br />
<br />
B.9<br />
<br />
C.5<br />
<br />
D.10Combinatoryhttps://gateoverflow.in/159137/p-and-c-doubtWed, 11 Oct 2017 05:22:55 +0000#self_doubt #
https://gateoverflow.in/158921/%23self_doubt-%23
1.how many outcome are appear if the dice thrown 10 times ?<br />
and<br />
2.how many way to arrange (1,2,3....13) into 8x8 matrix <br />
<br />
#doubt _both are looking same question but in 1st we apply diffrent method and in 2nd we apply diff so <br />
can we avoid these type of doubt...Combinatoryhttps://gateoverflow.in/158921/%23self_doubt-%23Tue, 10 Oct 2017 06:38:37 +0000generating function
https://gateoverflow.in/158597/generating-function
<p><strong>generating function shifted Fibonacci sequence</strong> </p>
<p>(what we actually do while finding generating function)</p>Combinatoryhttps://gateoverflow.in/158597/generating-functionMon, 09 Oct 2017 09:47:29 +0000discrete mathematics doubt .!
https://gateoverflow.in/158525/discrete-mathematics-doubt
What is the generating function for the sequence of Fibonacci numbers?Combinatoryhttps://gateoverflow.in/158525/discrete-mathematics-doubtMon, 09 Oct 2017 06:17:25 +0000UGCNET-Jan2017-II-4
https://gateoverflow.in/158417/ugcnet-jan2017-ii-4
How many multiples of 6 are there between the following pairs of numbers ?<br />
<br />
0 and 100 and –6 and 34<br />
<br />
(1) 16 and 6<br />
<br />
(2) 17 and 6<br />
<br />
(3) 17 and 7<br />
<br />
(4) 16 and 7Combinatoryhttps://gateoverflow.in/158417/ugcnet-jan2017-ii-4Sun, 08 Oct 2017 21:07:34 +0000# doubt
https://gateoverflow.in/158148/%23-doubt
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8333537619035037763"></p>Combinatoryhttps://gateoverflow.in/158148/%23-doubtSat, 07 Oct 2017 14:14:15 +0000combinatory
https://gateoverflow.in/158141/combinatory
Consider all possible permutations of eight distinct elements a, b, c, d, e, f, g, h. In how many of them, will d appear before b? Note that d and b may not necessarily be consecutive.Combinatoryhttps://gateoverflow.in/158141/combinatorySat, 07 Oct 2017 13:59:40 +0000kenneth rosen relations
https://gateoverflow.in/158028/kenneth-rosen-relations
How many of the 16 different relations on {0,1} contain the pair (0,1)?Combinatoryhttps://gateoverflow.in/158028/kenneth-rosen-relationsSat, 07 Oct 2017 07:01:40 +0000testbook test series
https://gateoverflow.in/158006/testbook-test-series
<p><strong>number of string of length 3 using 4 distinct alphabet...</strong></p>
<p><strong>including string of length zero and what if dont.? </strong></p>
<p> </p>Combinatoryhttps://gateoverflow.in/158006/testbook-test-seriesSat, 07 Oct 2017 06:02:38 +0000combinatorics
https://gateoverflow.in/157026/combinatorics
que- in how many way can 7 girl are seated at a round table so that 2 particular girl are seprated ???Combinatoryhttps://gateoverflow.in/157026/combinatoricsTue, 03 Oct 2017 16:55:04 +0000ace test
https://gateoverflow.in/156331/ace-test
How many ways consonant and vowels can be arranged alternatively for letters of word CONSTITUTION .Combinatoryhttps://gateoverflow.in/156331/ace-testSat, 30 Sep 2017 10:57:51 +0000Combinatorics
https://gateoverflow.in/155157/combinatorics
The letters of the word ALLAHABAD are rearranged to form new words and put in a dictionary. If the dictionary has only these words and one word on every page in alphabetical order then what is the page number on which the word LABADALAH comes?Combinatoryhttps://gateoverflow.in/155157/combinatoricsTue, 26 Sep 2017 02:07:08 +0000Combinatorics
https://gateoverflow.in/155155/combinatorics
Three variables x,y,z have a sum of 30. All three of them are non=negative integers. If any two variables don't have the same value and exactly one variable has a value of less than or equal to three, then find the number of possible solutions for the variables.Combinatoryhttps://gateoverflow.in/155155/combinatoricsTue, 26 Sep 2017 02:03:49 +0000KENNETH- rosen book excercise
https://gateoverflow.in/154910/kenneth-rosen-book-excercise
How many solutions are there to the equation <br />
<br />
x1 + x2 + x3 + x4 + x5 = 21 where 0 <= x1 <= 3 , 1 <= x2 < 4 and x3 >= 15 ?Combinatoryhttps://gateoverflow.in/154910/kenneth-rosen-book-excerciseMon, 25 Sep 2017 03:31:26 +0000Simple recurrence relation question
https://gateoverflow.in/154479/simple-recurrence-relation-question
<p>Given a sequence 2,3,4...n, which of the following is correct recurrence relation ?</p>
<p>1) T<sub>n</sub> = n+1;</p>
<p>2) T<sub>n</sub>=2a<sub>n-1</sub> + a<sub>n-2</sub></p>
<p>In recurrence relation, is it necessary that in the equation, the terms should <strong>always</strong> depend on previous terms ? Can 1) not be an answer?</p>
<p> </p>Combinatoryhttps://gateoverflow.in/154479/simple-recurrence-relation-questionSat, 23 Sep 2017 11:20:47 +0000generating function
https://gateoverflow.in/154462/generating-function
Let p be an odd prime number. Find the number of subsets A of the set {1, 2, …, 2p} such that<br />
<br />
(i) A has exactly p elements, and<br />
<br />
(ii) the sum of all the elements in A is divisible by p.Combinatoryhttps://gateoverflow.in/154462/generating-functionSat, 23 Sep 2017 10:26:24 +0000PERMUTATIONS
https://gateoverflow.in/153020/permutations
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10393981935072026539"></p>Combinatoryhttps://gateoverflow.in/153020/permutationsSun, 17 Sep 2017 19:43:01 +0000doubt
https://gateoverflow.in/152871/doubt
Suppose that we draw a card from a deck of 52 cards and replace it before the next draw. In how many ways can 10 cards be drawn so that the tenth card is a repetition of a previous draw.Combinatoryhttps://gateoverflow.in/152871/doubtSun, 17 Sep 2017 08:43:37 +0000combinatorics
https://gateoverflow.in/152594/combinatorics
<h1>10 persons are seated at round table. The number of ways of selecting 3 persons out of them if no two persons are adjacent to each other is?</h1>Combinatoryhttps://gateoverflow.in/152594/combinatoricsSat, 16 Sep 2017 09:05:03 +0000P& c doubt
https://gateoverflow.in/152083/p%26-c-doubt
In a room filled with 7 people ,4 people have exactly 1 Sibling in the room and three people have exactly two sibling in the room .if two individuals are selected from the room at random what is the probability that those two individuals are not sibling?<br />
<br />
5/21<br />
<br />
3/7<br />
<br />
4/7<br />
<br />
5/7<br />
<br />
16/21Combinatoryhttps://gateoverflow.in/152083/p%26-c-doubtThu, 14 Sep 2017 08:49:43 +0000P & C doubt
https://gateoverflow.in/152081/p-%26-c-doubt
Vijay wrote 4 different letter to send to 4 different addresses .for each letter, he prepared one envelope with its correct address. if the four letters are to be put into 4 envelopes at random in how many ways can we put the letters so that only two of the letter goes to the right envelope?<br />
<br />
2<br />
<br />
4<br />
<br />
1<br />
<br />
6Combinatoryhttps://gateoverflow.in/152081/p-%26-c-doubtThu, 14 Sep 2017 08:43:33 +0000bipartite graph
https://gateoverflow.in/151326/bipartite-graph
a)G={V,E} be bipartite graph and vertex partition V={V1, V2} if suppose number of vertices in V1 is 3 and V2 is 4 then number of bipartite graphs from V1 to V2 is ____________<br />
<br />
b)G={V,E} be bipartite graph and vertex partition V={V1, V2} if suppose number of vertices in V1 is 3 and V2 is 4 then number of complete bipartite graphs from V1 to V2 is ____________Combinatoryhttps://gateoverflow.in/151326/bipartite-graphMon, 11 Sep 2017 07:20:03 +0000combinatorics
https://gateoverflow.in/151188/combinatorics
The number of even permutations of the multiset {1,1,2} is ___ .Combinatoryhttps://gateoverflow.in/151188/combinatoricsSun, 10 Sep 2017 12:12:02 +0000Binomial theorem doubt
https://gateoverflow.in/150953/binomial-theorem-doubt
Find the set of values of x for which expansion of <br />
<br />
(9+ 5x)^ -1/2<br />
<br />
Is valid in ascending powers of x.<br />
<br />
a)(0,9/5)<br />
<br />
b)(-9/5,0)<br />
<br />
c)(-9/5,9/5)<br />
<br />
d)noneCombinatoryhttps://gateoverflow.in/150953/binomial-theorem-doubtSat, 09 Sep 2017 11:37:04 +0000Permutation and combination doubt
https://gateoverflow.in/150442/permutation-and-combination-doubt
In how many ways 3 friends ram ,rajat and rupesh having 6 one rupee coins, 7 one rupee coins ,8 one rupee coins respectively donate 10 rupees collectively.<br />
<br />
a)40<br />
<br />
b)45<br />
<br />
c)47<br />
<br />
d)50Combinatoryhttps://gateoverflow.in/150442/permutation-and-combination-doubtThu, 07 Sep 2017 09:19:30 +0000self doubt
https://gateoverflow.in/150107/self-doubt
find no of primes not exceeding 100 by inclusion exclusion principleCombinatoryhttps://gateoverflow.in/150107/self-doubtTue, 05 Sep 2017 15:06:47 +0000Rosen Excercise 6.2
https://gateoverflow.in/149744/rosen-excercise-6-2
Show that if five integers are selected from the first eight positive integers, there must be a pair of these integers with a sum equal to 9. <br />
<br />
can i choose same interger five times? ex. if i choose integer 1 five times.Combinatoryhttps://gateoverflow.in/149744/rosen-excercise-6-2Mon, 04 Sep 2017 08:13:01 +0000NPTEL Question
https://gateoverflow.in/149583/nptel-question
<p><strong>Find the particular solution of the given Recurrence relation or Difference equation.</strong></p>
<p><strong>a<sub>r</sub></strong><strong><sub> </sub>- 5a<sub>r-1 </sub>+ 6a<sub>r-2</sub> = 2<sup>r</sup> + r</strong></p>Combinatoryhttps://gateoverflow.in/149583/nptel-questionSun, 03 Sep 2017 14:29:02 +0000kenneth rosen
https://gateoverflow.in/149090/kenneth-rosen
<p>x1+x2+x3+x4+x5=21</p>
<hr>
<p>how many solution are there to the equation if</p>
<p>$0\leq$ x1 $\leq 3$ ,$1\leq$ x2$< 4$ and x3$\geq 15$</p>Combinatoryhttps://gateoverflow.in/149090/kenneth-rosenFri, 01 Sep 2017 12:18:38 +0000Pigeonhole Principle
https://gateoverflow.in/148816/pigeonhole-principle
During a month with 30 days, a baseball team plays at least one game a day, but no more<br />
than 45 games. Show that there must be a period of some number of consecutive days during<br />
which the team must play exactly 14 games.Combinatoryhttps://gateoverflow.in/148816/pigeonhole-principleThu, 31 Aug 2017 12:41:24 +0000self doubt
https://gateoverflow.in/147632/self-doubt
how many subsets of a set with 100 elements have more than one element?<br />
<br />
answer should be 2^(100)-1 ot it should be 2^(100)-101 which one correct?Combinatoryhttps://gateoverflow.in/147632/self-doubtSun, 27 Aug 2017 07:05:32 +0000self doubt
https://gateoverflow.in/147525/self-doubt
how many among the first 500,000 positive integer contain exactly one of each 3 , 4 and 5 in their decimal representationCombinatoryhttps://gateoverflow.in/147525/self-doubtSat, 26 Aug 2017 18:33:58 +0000Discrete mathematics
https://gateoverflow.in/145668/discrete-mathematics
what will be the number of even permutations of n objects? <br />
<br />
Explain!Combinatoryhttps://gateoverflow.in/145668/discrete-mathematicsSun, 20 Aug 2017 06:14:05 +0000rosen example 20
https://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?Combinatoryhttps://gateoverflow.in/144877/rosen-example-20Thu, 17 Aug 2017 09:06:46 +0000UPSC prelim test
https://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>Combinatoryhttps://gateoverflow.in/144083/upsc-prelim-testMon, 14 Aug 2017 11:16:58 +0000#combinotirics
https://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??Combinatoryhttps://gateoverflow.in/143639/%23combinotiricsSat, 12 Aug 2017 17:39:46 +0000counting
https://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>Combinatoryhttps://gateoverflow.in/143079/countingThu, 10 Aug 2017 16:53:03 +0000General Combinatorics
https://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>Combinatoryhttps://gateoverflow.in/142942/general-combinatoricsThu, 10 Aug 2017 07:34:30 +0000Sheldon Ross - Probability (2nd chapter)
https://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>Combinatoryhttps://gateoverflow.in/141823/sheldon-ross-probability-2nd-chapterSat, 05 Aug 2017 07:41:33 +0000Seldon Ross
https://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?Combinatoryhttps://gateoverflow.in/140617/seldon-rossSun, 30 Jul 2017 05:42:57 +0000Seldon Ross
https://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?Combinatoryhttps://gateoverflow.in/140615/seldon-rossSun, 30 Jul 2017 05:38:36 +0000combinatory
https://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 partCombinatoryhttps://gateoverflow.in/140181/combinatoryThu, 27 Jul 2017 08:49:54 +0000combinatory
https://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?Combinatoryhttps://gateoverflow.in/140179/combinatoryThu, 27 Jul 2017 08:41:29 +0000#gate
https://gateoverflow.in/139847/%23gate
Any good resource on Generating function and recurrrence relations ?Combinatoryhttps://gateoverflow.in/139847/%23gateTue, 25 Jul 2017 16:38:41 +0000