Recent questions in Combinatory

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1

#gate
Any good resource on Generating function and recurrrence relations ?

asked 1 day ago in Combinatory by saxena0612 (59 points) | 7 views

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2

Is Summation topic in GATE syllabus

asked 3 days ago in Combinatory by iarnav Active (1.5k points) | 8 views

+1 vote

1 answer

3

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?

asked 4 days ago in Combinatory by Shubhanshu Loyal (2.8k points) | 33 views

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4

Combination(Repetition) followed by Permutation(Repetition)

asked 5 days ago in Combinatory by Shubhanshu Loyal (2.8k points) | 14 views

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2 answers

5

Discreate Random Variable (Rose_8th Edition)

asked Jul 18 in Combinatory by Shubhanshu Loyal (2.8k points) | 21 views

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1 answer

6

Generating Function Question
I got (x^20).1/(1+x).1/(1-x)^3 . Now, if I write this as - [x^20].(1+x)^-1.(1-x)^-3 Now, I don't know how to solve this further when we have both factors having negative n. Please ... me here - http://gateoverflow.in/65803/find-number-integral-solutions-using-generating-function As i Didn't get that solution. Someone please simplify it.

asked Jul 16 in Combinatory by iarnav Active (1.5k points) | 42 views

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7

How to find this coefficient in this question?

asked Jul 15 in Combinatory by iarnav Active (1.5k points) | 29 views

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1 answer

8

Question on Number System
Find the remainder of $\frac{9^{1}+9^{2}+...+9^{n}}{6}$ where $n$ is multiple of 11. I am getting $0$ or $3$. But given answer is 3. Can anyone check?

asked Jul 13 in Combinatory by Aghori Loyal (3.7k points) | 26 views

+1 vote

1 answer

9

Question on Number System.
If $N = 1!+2!+3!+...+10!$. What is the last digit of $N^{N}$?

asked Jul 13 in Combinatory by Aghori Loyal (3.7k points) | 29 views

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10

rosen #section 5.5 question 15(d) page no 378 [closed]

asked Jul 12 in Combinatory by Vishal Rao (21 points) | 23 views

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1 answer

11

rosen Exer:5.5 15(c) how many solutions are there for x1+x2+x3+x4+x5=21 such that 0<=x1<=10?(detailed explanation) [closed]

asked Jul 12 in Combinatory by Vishal Rao (21 points) | 40 views

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1 answer

12

rosen exercise problem
How many bit strings of length 10 contain at least three 1s and at least three 0s? My Approach:-> using product rule There are 3 subtask following (filling 3 ones in 10 places) = (filling 3 zeros in remaing 7 places) = (filling ... is greater than (total number of string). Now , i want to know what is wrong in my apporach. please explain..

asked Jul 11 in Combinatory by indrajeet Active (1.6k points) | 17 views

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2 answers

13

Kenneth Rosen Counting 6.5 Example 6

asked Jul 11 in Combinatory by Aswath K (119 points) | 53 views

+1 vote

1 answer

14

gatebook
How many bit strings of length 6 have more no of zeros than ones?? We can solve this drawing tree but it takes so much time Is there any other way??

asked Jul 9 in Combinatory by Niharika 1 Active (1.2k points) | 26 views

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1 answer

15

GATEbook

asked Jul 9 in Combinatory by Niharika 1 Active (1.2k points) | 35 views

+1 vote

1 answer

16

Gatebook
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

asked Jul 9 in Combinatory by Niharika 1 Active (1.2k points) | 30 views

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1 answer

17

Rosen Counting Permutations
I was doing two Questions of rosen counting chapter 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 ? Answer is 2(n!)^2, I agree with logic and ... from (n+1) places created my positioning the men and permuting them again i.e P(n,n)*P(n+1,n) ??

asked Jul 8 in Combinatory by bhuv (343 points) | 24 views

+3 votes

1 answer

18

Discrete Mathematics for Computer Scientists and Mathematicians , Chapter- 2 , Exercise- 2.2, Question-4

asked Jul 3 in Combinatory by Ankita Choudhary (65 points) | 69 views

+1 vote

0 answers

19

Discrete Mathematics for Computer Scientists and Mathematicians , Chapter- 2 , Exercise- 2.1, Question-36

asked Jul 3 in Combinatory by Ankita Choudhary (65 points) | 69 views

+1 vote

0 answers

20

Equal coefficients
$\begin{align*} &A = \left ( p x + q \right )^{504} \text{ where p and q are +ve integers and }gcd(p,q) = 1 \\ &\text{Given } \left [ x^4 \right ] = \left [ x^5 \right ] , \text{ where } \left [ x^k \right ] \text{ denote the coefficient of }x^k \text{ in A.} \\ &\text{What is p+q ?} \end{align*}$

asked Jul 1 in Combinatory by Debashish Deka Veteran (50.5k points) | 19 views

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1 answer

21

Sheldon Ross Chapter 1 Example 3c

asked Jun 27 in Combinatory by thehobo03 (199 points) | 20 views

+2 votes

1 answer

22

combinatorial argument
$\begin{align*} &\text{Prove using combinatorial argument } \\ &1) \qquad \text{For } n \geq k \geq 0 \qquad \left ( n-k \right )\cdot \binom{n}{k} = n \cdot \binom{n-1}{k} \\ &2) \qquad \text{For } n \geq 2 \qquad \quad k \cdot (k-1) \cdot \binom{n}{k} = n \cdot (n-1) \cdot \binom{n-2}{k-2} \\ \end{align*}$

asked Jun 27 in Combinatory by Debashish Deka Veteran (50.5k points) | 36 views

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0 answers

23

Integer Sequence
$\begin{align*} &\text{A} = \text{Set of integer sequence }\left ( a_1,a_2,a_2 ,\dots , a_k \right ) \\ &\text{where } 1 \leq a_1 \leq a_2 \leq a_3 \leq \dots \leq a_k \leq n \\ &\text{B} = \text{Set of integer sequence }\left ( ... ; b_2 < b_3 < \dots < b_k \leq n \\ \end{align*}$ Prove that $\begin{align*} |A| = |B| \end{align*}$

asked Jun 27 in Combinatory by Debashish Deka Veteran (50.5k points) | 16 views

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24

Combinatoric properties
Prove that : $\begin{align*} &\text{For n , k , m are integers and } 0 < m \leq k < n \\ &\text{GCD}\left [ \binom{n}{m},\binom{n}{k} \right ] > 1 \\ \end{align*}$

asked Jun 27 in Combinatory by Debashish Deka Veteran (50.5k points) | 12 views

+1 vote

1 answer

25

Combinatory
How many ordered quadruples $\left ( x_{1},x_{2},x_{3},x_{4} \right )$ of odd positive integers satisfy $$x_{1}+x_{2}+x_{3}+x_{4}=98?$$

asked Jun 24 in Combinatory by parulk (123 points) | 61 views

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1 answer

26

Recurrence Relation
The solution of an = 2an-1 + 1 where a0 = 1 is ? Please use the substitution method because I seem to have problem understanding it.

asked Jun 24 in Combinatory by thehobo03 (199 points) | 15 views

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27

Combinatorics : Multinomial Coefficients

asked Jun 24 in Combinatory by Vasu Srivastava (87 points) | 46 views

+1 vote

1 answer

28

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 i. no letter is correctly placed? ii. at least 1 letter is correctly placed? iii. exactly 2 letters ... placed? iv. at most 1 letter is correctly placed? v. at least 1 letter is wrongly placed? vi. exactly 1 letter is wrongly placed?

asked Jun 23 in Combinatory by thehobo03 (199 points) | 38 views

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1 answer

29

#combinatory
Determine the number of factors of 34 * 52 * * 117 * 138.

asked Jun 19 in Combinatory by Nachiket Karambelkar (165 points) | 46 views

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1 answer

30

#Discrete #Combinatorics
The number of ways in which n distinct objects can be put into two identical boxes so that no box remains empty, is a) 2^n - 1 b) 2^n - 2 c) 2^(n-1) - 1 d) None of these Please explain your answer.

asked Jun 11 in Combinatory by Jatin18 (91 points) | 63 views

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