List questions from binomial-coefficients

395

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A combinatorial identity: $\sum_{k=0}^j (-1)^k \frac{n-2k}{n-j-k} \binom{n}{k} \binom{n-j-k}{j-k} = 0$

Published on 22 Mar 2026 - 18:35

67

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How can I find a short term for those sums?

Published on 25 Mar 2026 - 10:55

811

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Binomial coefficients- how to work out 0.5 choose 2

Published on 22 Mar 2026 - 22:30

53

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Solving the following:

Published on 22 Mar 2026 - 22:15

75

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Combinatorics Binomial How to prove it?

Published on 26 Mar 2026 - 4:28

63

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Can $\sum_{i=a}^{b}p^{i}\binom{i}{a}\binom{b}{i}$ be simplified?

Published on 22 Mar 2026 - 23:52

47

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How to solve binomial sum but with denominator

Published on 23 Mar 2026 - 15:59

165

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Choosing 80 from 100

Published on 25 Mar 2026 - 20:33

85

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Prove that $\sum_{j=k}^{2k}(-1)^j\binom{n-j}{i}\binom{k}{j-k} =(-1)^k \binom{n-2k}{i-k}$

Published on 23 Mar 2026 - 5:45

73

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Closed form for $\sum_{i=1}^{n}\binom{n}{i}\frac{x^{i}}{i}$

Published on 25 Mar 2026 - 9:53

142

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Calculate binomial sum

Published on 23 Mar 2026 - 8:27

640

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Binomial coefficient real life example.

Published on 23 Mar 2026 - 4:08

139

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What are the odds of winning a lottery, if I insist on always playing a certain number?

Published on 25 Mar 2026 - 18:14

862

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Proving an Upper Bound on the Number of Partitions of $n$ into $m$ Parts

Published on 25 Mar 2026 - 10:59

460

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Behavior of $\sum_{k=0}^n (-1)^k {2n \choose k} (1-\frac{k}{n})^2 \ln(1-\frac{k}{n})$

Published on 23 Mar 2026 - 1:42

List Question

A combinatorial identity: $\sum_{k=0}^j (-1)^k \frac{n-2k}{n-j-k} \binom{n}{k} \binom{n-j-k}{j-k} = 0$

How can I find a short term for those sums?

Binomial coefficients- how to work out 0.5 choose 2

Solving the following:

Combinatorics Binomial How to prove it?

Can $\sum_{i=a}^{b}p^{i}\binom{i}{a}\binom{b}{i}$ be simplified?

How to solve binomial sum but with denominator

Choosing 80 from 100

Prove that $\sum_{j=k}^{2k}(-1)^j\binom{n-j}{i}\binom{k}{j-k} =(-1)^k \binom{n-2k}{i-k}$

Closed form for $\sum_{i=1}^{n}\binom{n}{i}\frac{x^{i}}{i}$

Calculate binomial sum

Binomial coefficient real life example.

What are the odds of winning a lottery, if I insist on always playing a certain number?

Proving an Upper Bound on the Number of Partitions of $n$ into $m$ Parts

Behavior of $\sum_{k=0}^n (-1)^k {2n \choose k} (1-\frac{k}{n})^2 \ln(1-\frac{k}{n})$

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