List questions from binomial-coefficients

Published on 08 Dec 2018 - 22:16

59

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Is there a formula to get the total wins from odds combination?

Published on 25 Mar 2026 - 3:19

435

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Recurrence relation for 2nCn

Published on 10 Dec 2018 - 9:39

111

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How to compute $\sum_{j=1}^{n} {{n}\choose {j}} \cdot (-1)^{j+1} \cdot \frac{(n-j)^{n-1}}{n^{n-1}}$

Published on 10 Dec 2018 - 11:11

7.5k

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A combination of three dice

Published on 26 Mar 2026 - 17:18

216

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Moment generating function of a binary variable

Published on 25 Mar 2026 - 18:59

150

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Evaluate $\sum_{n=1}^N n {n \choose k}$ and get a closed form solution

Published on 27 Mar 2026 - 20:19

342

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Proof for this binomial coefficient's equation

Published on 12 Dec 2018 - 9:58

381

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Half of Vandermonde's Identity

Published on 12 Dec 2018 - 23:07

247

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Combinatorial identity: summation of stars and bars

Published on 13 Dec 2018 - 18:59

73

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Proving a binomial series to be $2^n$

Published on 14 Dec 2018 - 4:16

154

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Given that $\binom{16}r =\binom{16}{2r + 1}$, what is the value of $r$?

Published on 15 Dec 2018 - 9:24

187

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Combinations without repetition and with limit on consecutives

Published on 15 Dec 2018 - 17:42

111

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Evaluate:$\frac{1}{2^{101}}\sum_{k=1}^{51} \sum_{r=0}^{k-1}\binom{51}{k}\binom{50}{r}$

Published on 26 Mar 2026 - 4:53

1.7k

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How to prove upper bound for partial sum of binomial coefficients

Published on 17 Dec 2018 - 14:55

List Question

Explanation of the Wolstenholme theorem proof

Is there a formula to get the total wins from odds combination?

Recurrence relation for 2nCn

How to compute $\sum_{j=1}^{n} {{n}\choose {j}} \cdot (-1)^{j+1} \cdot \frac{(n-j)^{n-1}}{n^{n-1}}$

A combination of three dice

Moment generating function of a binary variable

Evaluate $\sum_{n=1}^N n {n \choose k}$ and get a closed form solution

Proof for this binomial coefficient's equation

Half of Vandermonde's Identity

Combinatorial identity: summation of stars and bars

Proving a binomial series to be $2^n$

Given that $\binom{16}r =\binom{16}{2r + 1}$, what is the value of $r$?

Combinations without repetition and with limit on consecutives

Evaluate:$\frac{1}{2^{101}}\sum_{k=1}^{51} \sum_{r=0}^{k-1}\binom{51}{k}\binom{50}{r}$

How to prove upper bound for partial sum of binomial coefficients

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