Question

Give a combinatorial proof for $\binom {n}{r}\binom {r}{k} = \binom {n}{k} \binom {n-k}{r-k}$

score 735 · Answer 1 · 2021-10-15 02:52:24

735

Views

Give a combinatorial proof for $\binom {n}{r}\binom {r}{k} = \binom {n}{k} \binom {n-k}{r-k}$

Published on 15 Oct 2021 - 2:52

score 86 · Answer 2 · 2021-10-18 15:22:51

86

Views

Given the final points of all teams in a sports league, counting the number of possibilities that would lead to it

Published on 18 Oct 2021 - 15:22

score 525 · Answer 3 · 2021-10-18 23:46:19

525

Views

Give a combinatorial proof for $n^2 = n(n-1)+n$

Published on 18 Oct 2021 - 23:46

score 128 · Answer 4 · 2021-10-19 06:36:13

128

Views

Combinatorial argument for a homework question: $\binom nr \binom r3=\binom n3\binom{n-3}{r-3}$

Published on 19 Oct 2021 - 6:36

score 310 · Answer 5 · 2021-10-20 20:09:27

310

Views

Examples of nCr (combinations) notation

Published on 20 Oct 2021 - 20:09

score 48 · Answer 6 · 2021-10-22 23:43:01

48

Views

An inequality for combination sums

Published on 22 Oct 2021 - 23:43

score 230 · Answer 7 · 2026-03-30 15:18:01

230

Views

Combinatorial proof calculating the expected minimum of uniform IID random variables (first order statistic)

Published on 30 Mar 2026 - 15:18

score 66 · Answer 8 · 2021-11-02 17:07:58

66

Views

Analogy between two similar problems in Combinatorics

Published on 02 Nov 2021 - 17:07

score 103 · Answer 9 · 2021-11-03 03:26:50

103

Views

In need of a combinatorial proof of $12 + 23 + 34 + ... + n(n+1) = 2{n+2\choose 3}$

Published on 03 Nov 2021 - 3:26

score 271 · Answer 10 · 2021-11-04 17:37:25

271

Views

Combinatorial Identity for Binomial Expression

Published on 04 Nov 2021 - 17:37

score 135 · Answer 11 · 2021-11-07 17:29:53

135

Views

Combinatorial proof of $P_r^{n+1}=r!+r(P_{r-1}^n+P_{r-1}^{n-1}+\cdots+P_{r-1}^r)$

Published on 07 Nov 2021 - 17:29

score 136 · Answer 12 · 2021-11-08 15:10:41

136

Views

Product of some binomial coefficients

Published on 08 Nov 2021 - 15:10

score 183 · Answer 13 · 2026-03-30 03:37:28

183

Views

Stirling Numbers of the Second Kind: Combinatorial Proof

Published on 30 Mar 2026 - 3:37

score 157 · Answer 14 · 2021-11-12 10:22:41

157

Views

About the Fibonacci's numbers identity ${n \choose k}_F = F_{n-k+1}{n-1 \choose k-1}_F+F_{k-1} {n-1 \choose k}_F$

Published on 12 Nov 2021 - 10:22

score 84 · Answer 15 · 2021-11-12 11:41:19

84

Views

A combinatorics problem with applications for optimizing Huffman Compression Algorithms

Published on 12 Nov 2021 - 11:41

List Question

Give a combinatorial proof for $\binom {n}{r}\binom {r}{k} = \binom {n}{k} \binom {n-k}{r-k}$

Given the final points of all teams in a sports league, counting the number of possibilities that would lead to it

Give a combinatorial proof for $n^2 = n(n-1)+n$

Combinatorial argument for a homework question: $\binom nr \binom r3=\binom n3\binom{n-3}{r-3}$

Examples of nCr (combinations) notation

An inequality for combination sums

Combinatorial proof calculating the expected minimum of uniform IID random variables (first order statistic)

Analogy between two similar problems in Combinatorics

In need of a combinatorial proof of $12 + 23 + 34 + ... + n(n+1) = 2{n+2\choose 3}$

Combinatorial Identity for Binomial Expression

Combinatorial proof of $P_r^{n+1}=r!+r(P_{r-1}^n+P_{r-1}^{n-1}+\cdots+P_{r-1}^r)$

Product of some binomial coefficients

Stirling Numbers of the Second Kind: Combinatorial Proof

About the Fibonacci's numbers identity ${n \choose k}_F = F_{n-k+1}{n-1 \choose k-1}_F+F_{k-1} {n-1 \choose k}_F$

A combinatorics problem with applications for optimizing Huffman Compression Algorithms

Trending Questions

Popular # Hahtags

Popular Questions