List questions from binomial-coefficients

Published on 12 Jan 2020 - 22:24

116

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Help in summing: $\sum_{k=m} ^{2m} ~k\cdot ~2^{-k} {k \choose m}$

Published on 14 Jan 2020 - 9:59

163

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Inequality $\binom{n+m}{k}+\binom{n-m}{k}\ge 2\binom{n}{k}$

Published on 14 Jan 2020 - 15:56

85

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Rewrite of binomial expression

Published on 30 Mar 2026 - 15:13

53

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Proving $(k+1)^n$ is equal to a nested summation with k many sigmas?

Published on 29 Mar 2026 - 19:33

129

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Interesting Binomial identity

Published on 17 Jan 2020 - 19:27

1.7k

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Sum of combinations formula

Published on 30 Mar 2026 - 15:10

101

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Probability of an event if r out of n events were true.

Published on 19 Jan 2020 - 8:16

180

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Prove that $\sum_{i=0}^{k}\binom{k-i}{b}\binom{i}{a-1}=\binom{k+1}{a+b}$

Published on 19 Jan 2020 - 18:24

127

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Combinatorial Proof ${n \choose k}\cdot (n-k)\cdot 2^{k} = \sum_{i=1}^{k+1} {n\choose i}\cdot{n-i\choose k-i+1}\cdot i $

Published on 26 Mar 2026 - 20:41

80

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How do I find the following finite sum?

Published on 21 Jan 2020 - 7:27

70

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Find number of red balls after K turns if you paint Q balls from a bag of N distinct ones

Published on 23 Feb 2026 - 12:09

502

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Identity involving falling factorial

Published on 29 Mar 2026 - 18:12

91

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Sum of binomial coefficients with powered variable

Published on 23 Jan 2020 - 7:10

376

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Cardinality of even and odd number of elements in Power Set

Published on 23 Jan 2020 - 15:35

List Question

Is there a sub-quadratic method of calculating the expanded polynomial from its roots?

Help in summing: $\sum_{k=m} ^{2m} ~k\cdot ~2^{-k} {k \choose m}$

Inequality $\binom{n+m}{k}+\binom{n-m}{k}\ge 2\binom{n}{k}$

Rewrite of binomial expression

Proving $(k+1)^n$ is equal to a nested summation with k many sigmas?

Interesting Binomial identity

Sum of combinations formula

Probability of an event if r out of n events were true.

Prove that $\sum_{i=0}^{k}\binom{k-i}{b}\binom{i}{a-1}=\binom{k+1}{a+b}$

Combinatorial Proof ${n \choose k}\cdot (n-k)\cdot 2^{k} = \sum_{i=1}^{k+1} {n\choose i}\cdot{n-i\choose k-i+1}\cdot i $

How do I find the following finite sum?

Find number of red balls after K turns if you paint Q balls from a bag of N distinct ones

Identity involving falling factorial

Sum of binomial coefficients with powered variable

Cardinality of even and odd number of elements in Power Set

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