Question

How many ways can you divide a group of people into boxes?

score 124 · Answer 1 · 2022-10-12 16:19:55

124

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How many ways can you divide a group of people into boxes?

Published on 12 Oct 2022 - 16:19

score 106 · Answer 2 · 2022-10-18 01:52:39

106

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Lattice path: proof of $\sum_{k=0}^n{s+k \choose k}{n-k \choose m}={s+n+1 \choose s+m+1}$

Published on 18 Oct 2022 - 1:52

score 80 · Answer 3 · 2026-03-29 10:36:14

80

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$X$ a finite set and $A_1,A_2,...,A_r$ be subsets of $X$ of size $m$. If $r < 2^{m-1}$, then $\exists$ a $2$-coloring of $X$ s.t. no $A_i$ is mono.

Published on 29 Mar 2026 - 10:36

score 73 · Answer 4 · 2022-10-24 23:58:00

73

Views

Using the combinational proof template for discrete mathematics is this a valid polished proof?

Published on 24 Oct 2022 - 23:58

score 157 · Answer 5 · 2022-10-28 00:56:10

157

Views

Confusion about combinatorial identity $k {n\choose k} = n{ {n-1}\choose{k-1} }$

Published on 28 Oct 2022 - 0:56

score 173 · Answer 6 · 2026-03-26 23:00:21

173

Views

Multinomial identity

Published on 26 Mar 2026 - 23:00

score 150 · Answer 7 · 2022-11-02 21:58:59

150

Views

Combinatorics proof of Abel's binomial theorem

Published on 02 Nov 2022 - 21:58

score 102 · Answer 8 · 2022-11-04 15:46:58

102

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Provide a combinatorial argument for the following: $2^n = \sum_{k\text{ odd}} \binom{n+1}{k}$

Published on 04 Nov 2022 - 15:46

score 75 · Answer 9 · 2022-11-11 12:12:57

75

Views

An identity between summations involving a binomial expansion.

Published on 11 Nov 2022 - 12:12

score 798 · Answer 10 · 2026-03-30 06:47:27

798

Views

Combinatorial proof of Stirling Numbers of the second kind

Published on 30 Mar 2026 - 6:47

score 90 · Answer 11 · 2022-11-14 01:24:18

90

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Does $\sum_{j=0}^n\sum_{k=0}^n\binom{j}{a}\binom{k}{b}\binom{n-j-k}{c}=\binom{n+1}{a+b+c+2}?$

Published on 14 Nov 2022 - 1:24

score 59 · Answer 12 · 2022-11-15 03:07:10

59

Views

Could someone please help me with this proof? Can't think of an idea

Published on 15 Nov 2022 - 3:07

score 154 · Answer 13 · 2022-11-19 16:34:19

154

Views

How to prove the binomial identity $\binom{n + 1}{a + b + 1} = \sum_{k = 0}^n \binom{k}{a}\binom{n - k}{b}$

Published on 19 Nov 2022 - 16:34

score 61 · Answer 14 · 2022-11-22 04:07:36

61

Views

Ways to colour elements of matrix using two colours

Published on 22 Nov 2022 - 4:07

score 73 · Answer 15 · 2022-11-22 05:27:37

73

Views

Number of ways to choose $m$ boys and $k$ girls from $n$ boys and $n$ girls?

Published on 22 Nov 2022 - 5:27

List Question

How many ways can you divide a group of people into boxes?

Lattice path: proof of $\sum_{k=0}^n{s+k \choose k}{n-k \choose m}={s+n+1 \choose s+m+1}$

$X$ a finite set and $A_1,A_2,...,A_r$ be subsets of $X$ of size $m$. If $r < 2^{m-1}$, then $\exists$ a $2$-coloring of $X$ s.t. no $A_i$ is mono.

Using the combinational proof template for discrete mathematics is this a valid polished proof?

Confusion about combinatorial identity $k {n\choose k} = n{ {n-1}\choose{k-1} }$

Multinomial identity

Combinatorics proof of Abel's binomial theorem

Provide a combinatorial argument for the following: $2^n = \sum_{k\text{ odd}} \binom{n+1}{k}$

An identity between summations involving a binomial expansion.

Combinatorial proof of Stirling Numbers of the second kind

Does $\sum_{j=0}^n\sum_{k=0}^n\binom{j}{a}\binom{k}{b}\binom{n-j-k}{c}=\binom{n+1}{a+b+c+2}?$

Could someone please help me with this proof? Can't think of an idea

How to prove the binomial identity $\binom{n + 1}{a + b + 1} = \sum_{k = 0}^n \binom{k}{a}\binom{n - k}{b}$

Ways to colour elements of matrix using two colours

Number of ways to choose $m$ boys and $k$ girls from $n$ boys and $n$ girls?

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