Question

Combinatorial identity $\sum_{k=0}^{n}\binom{n}{k}\binom{n}{k -1} = \binom{2n}{n+1}$

score 407 · Answer 1 · 2016-12-07 05:52:44

407

Views

Combinatorial identity $\sum_{k=0}^{n}\binom{n}{k}\binom{n}{k -1} = \binom{2n}{n+1}$

Published on 07 Dec 2016 - 5:52

score 73 · Answer 2 · 2016-12-07 21:03:13

73

Views

Which of these is larger by combinatorial reasoning

Published on 07 Dec 2016 - 21:03

score 118 · Answer 3 · 2017-01-02 15:29:52

118

Views

prove $\sum_{k=0}^{3n+2}\frac{(-1)^k}{6n+5-k}\binom{6n+5-k}{k}=\frac{1}{6n+5}$

Published on 02 Jan 2017 - 15:29

score 209 · Answer 4 · 2017-01-15 03:22:45

209

Views

Feller's Introduction to probability - Configuration of 7 balls in 7 cells

Published on 15 Jan 2017 - 3:22

score 208 · Answer 5 · 2026-03-26 04:50:57

208

Views

max-weighted sums of multinomial coefficent

Published on 26 Mar 2026 - 4:50

score 916 · Answer 6 · 2017-01-22 17:59:28

916

Views

Combinatorial proof of $\sum_{i=0}^n {n \choose i}^2={2n \choose n}$ by using a binary string of length $2n$

Published on 22 Jan 2017 - 17:59

score 719 · Answer 7 · 2017-01-25 03:40:37

719

Views

Explain how $\binom{n}{0}-\binom{n}{1}+\binom{n}{2}+...+(-1)^{n}\binom{n}{n} = 0$

Published on 25 Jan 2017 - 3:40

score 66 · Answer 8 · 2017-02-05 04:29:04

66

Views

Consider events $A, B, C$ such that $P(A\mid B) > P(A)$ and $P(B\mid C) > P(B)$.

Published on 05 Feb 2017 - 4:29

score 330 · Answer 9 · 2017-02-05 19:19:18

330

Views

Combinatorial argument with the binomial theorem: $\binom{n}{0} + \binom{n}{1} 2 + \binom{n}{2} 2^2 + ... + \binom{n}{n} {2^n}$

Published on 05 Feb 2017 - 19:19

score 123 · Answer 10 · 2017-02-07 23:13:48

123

Views

We are given that 15 boxes contain the total of 100 apples

Published on 07 Feb 2017 - 23:13

score 121 · Answer 11 · 2017-02-16 06:55:31

121

Views

help with combinatorial proof $\sum_{i=0}^r \left(\!\!{m\choose i}\!\!\right)= \binom{m+r}{r}$

Published on 16 Feb 2017 - 6:55

score 251 · Answer 12 · 2017-02-16 14:58:13

251

Views

Combinatorial proof for party-goers.

Published on 16 Feb 2017 - 14:58

score 193 · Answer 13 · 2017-02-27 18:28:44

193

Views

Combinatorial determinant & Vandermonde relation

Published on 27 Feb 2017 - 18:28

score 135 · Answer 14 · 2017-03-03 18:50:19

135

Views

Use combinatorial argument to prove the following identites:

Published on 03 Mar 2017 - 18:50

score 362 · Answer 15 · 2017-03-21 19:46:40

362

Views

Double counting proof of binomial theorem for positive integers $x,y$

Published on 21 Mar 2017 - 19:46

List Question

Combinatorial identity $\sum_{k=0}^{n}\binom{n}{k}\binom{n}{k -1} = \binom{2n}{n+1}$

Which of these is larger by combinatorial reasoning

prove $\sum_{k=0}^{3n+2}\frac{(-1)^k}{6n+5-k}\binom{6n+5-k}{k}=\frac{1}{6n+5}$

Feller's Introduction to probability - Configuration of 7 balls in 7 cells

max-weighted sums of multinomial coefficent

Combinatorial proof of $\sum_{i=0}^n {n \choose i}^2={2n \choose n}$ by using a binary string of length $2n$

Explain how $\binom{n}{0}-\binom{n}{1}+\binom{n}{2}+...+(-1)^{n}\binom{n}{n} = 0$

Consider events $A, B, C$ such that $P(A\mid B) > P(A)$ and $P(B\mid C) > P(B)$.

Combinatorial argument with the binomial theorem: $\binom{n}{0} + \binom{n}{1} 2 + \binom{n}{2} 2^2 + ... + \binom{n}{n} {2^n}$

We are given that 15 boxes contain the total of 100 apples

help with combinatorial proof $\sum_{i=0}^r \left(\!\!{m\choose i}\!\!\right)= \binom{m+r}{r}$

Combinatorial proof for party-goers.

Combinatorial determinant & Vandermonde relation

Use combinatorial argument to prove the following identites:

Double counting proof of binomial theorem for positive integers $x,y$

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