Question

Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$

score 171 · Answer 1 · 2016-08-11 18:38:28

171

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Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$

Published on 11 Aug 2016 - 18:38

score 205 · Answer 2 · 2026-03-30 20:48:31

205

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Combinatorial identity $\prod_{j=1}^n {n\choose j} =\prod_{k=1}^n {k^k\over k!}$

Published on 30 Mar 2026 - 20:48

score 190 · Answer 3 · 2026-03-31 06:00:31

190

Views

coefficient of $x^9$ in binominal expansion

Published on 31 Mar 2026 - 6:00

score 821 · Answer 4 · 2026-04-11 07:55:18

821

Views

Unusual Combinatorial Identity (Alternating Sum of Binomial Products)

Published on 11 Apr 2026 - 7:55

score 1.2k · Answer 5 · 2026-04-11 08:29:37

1.2k

Views

A nice formula for the Thue–Morse sequence

Published on 11 Apr 2026 - 8:29

score 156 · Answer 6 · 2016-08-14 19:42:57

156

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I have a algorithm and from the post its time complexity is: $\sum_{k=1}^{n}k\binom nk= n 2^{n-1}$

Published on 14 Aug 2016 - 19:42

score 264 · Answer 7 · 2026-04-11 07:31:31

264

Views

Asymptotic of binomial coefficients near the center

Published on 11 Apr 2026 - 7:31

score 113 · Answer 8 · 2016-08-16 06:23:24

113

Views

How to show this binomial equality is true/not: $\sum _{k=1}^m2^{2k-1}\binom{n}{2k-1}=\sum _{k=1}^m 2^{2k}\binom{n}{2k}$

Published on 16 Aug 2016 - 6:23

score 65 · Answer 9 · 2026-03-27 15:11:42

65

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Use combinations to explain why $C(n, k) = C(n, n-k)$ for any $n, k ∈ ℕ, 0 ≤ k ≤ n$.

Published on 27 Mar 2026 - 15:11

score 213 · Answer 10 · 2026-04-11 12:03:39

213

Views

Is Pascal's triangle valid in non-decimal systems?

Published on 11 Apr 2026 - 12:03

score 186 · Answer 11 · 2016-08-17 07:37:33

186

Views

Is it possible to find a set of 5 integers, such that the 10 sums each have a different last digit?

Published on 17 Aug 2016 - 7:37

score 45 · Answer 12 · 2026-03-25 22:01:46

45

Views

Counting functions and subsets

Published on 25 Mar 2026 - 22:01

score 133 · Answer 13 · 2016-08-18 21:20:43

133

Views

Factors of $\binom{2^{q}}{2}-1$ and Wagstaff Primes

Published on 18 Aug 2016 - 21:20

score 20k · Answer 14 · 2026-04-11 13:38:04

20k

Views

Can the number of diagonals of a given polygon be found using combinations?

Published on 11 Apr 2026 - 13:38

score 462 · Answer 15 · 2016-08-19 10:34:30

462

Views

Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$

Published on 19 Aug 2016 - 10:34

List Question

Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$

Combinatorial identity $\prod_{j=1}^n {n\choose j} =\prod_{k=1}^n {k^k\over k!}$

coefficient of $x^9$ in binominal expansion

Unusual Combinatorial Identity (Alternating Sum of Binomial Products)

A nice formula for the Thue–Morse sequence

I have a algorithm and from the post its time complexity is: $\sum_{k=1}^{n}k\binom nk= n 2^{n-1}$

Asymptotic of binomial coefficients near the center

How to show this binomial equality is true/not: $\sum _{k=1}^m2^{2k-1}\binom{n}{2k-1}=\sum _{k=1}^m 2^{2k}\binom{n}{2k}$

Use combinations to explain why $C(n, k) = C(n, n-k)$ for any $n, k ∈ ℕ, 0 ≤ k ≤ n$.

Is Pascal's triangle valid in non-decimal systems?

Is it possible to find a set of 5 integers, such that the 10 sums each have a different last digit?

Counting functions and subsets

Factors of $\binom{2^{q}}{2}-1$ and Wagstaff Primes

Can the number of diagonals of a given polygon be found using combinations?

Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$

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