List questions from binomial-coefficients

Published on 02 Apr 2026 - 13:40

64

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How do I prove that $\sum_{\ell\text{ odd}}^{n} \binom{n}{\ell} = 2^{n-1}$?

Published on 06 Jul 2020 - 15:47

679

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simple method for expanding binomial with 3 or more terms?

Published on 07 Jul 2020 - 5:18

357

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Identity for a sum of product of binomial coefficients

Published on 07 Jul 2020 - 12:49

75

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Binomial theorem and logarithms

Published on 06 Apr 2026 - 18:58

88

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find the coefficient of $x^5$ in $(1+2x-3x^2)^6$

Published on 08 Jul 2020 - 2:31

65

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Evaluate $\displaystyle\sum_{r=0}^8 (-1)^r \binom{20}{r} \binom{20}{8-r}$

Published on 30 Mar 2026 - 16:25

104

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A Question on "Stars and Bars" and why it doesn't apply to a problem asked earlier today.

Published on 11 Jul 2020 - 23:42

73

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Simplifying $ {m\choose l}^{-1}\sum_ii^p{n\choose i}{m-n\choose l-i} $

Published on 13 Jul 2020 - 17:59

53

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Trying to simplify $ \sum_{k=1}^n{n\choose k}\frac{1}{k^l}p^k(1-p)^{n-k}. $

Published on 28 Mar 2026 - 14:19

108

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Sum of product of two combinations

Published on 14 Jul 2020 - 10:56

83

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Number of subsets $S \subset A_1 \cup A_2 \cup ... A_n$ where $|S \cap A_i| = a_i$?

Published on 26 Mar 2026 - 4:53

66

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An approximation of combinatorials using the geometric mean?

Published on 23 Feb 2026 - 11:47

63

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Prove binomial coefficient

Published on 15 Jul 2020 - 10:46

1.1k

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What is the number of $6$ digit positive integers whose sum of the digits is at least $52$?

Published on 25 Mar 2026 - 1:18

List Question

Modified central binomial coefficients generating function

How do I prove that $\sum_{\ell\text{ odd}}^{n} \binom{n}{\ell} = 2^{n-1}$?

simple method for expanding binomial with 3 or more terms?

Identity for a sum of product of binomial coefficients

Binomial theorem and logarithms

find the coefficient of $x^5$ in $(1+2x-3x^2)^6$

Evaluate $\displaystyle\sum_{r=0}^8 (-1)^r \binom{20}{r} \binom{20}{8-r}$

A Question on "Stars and Bars" and why it doesn't apply to a problem asked earlier today.

Simplifying $ {m\choose l}^{-1}\sum_ii^p{n\choose i}{m-n\choose l-i} $

Trying to simplify $ \sum_{k=1}^n{n\choose k}\frac{1}{k^l}p^k(1-p)^{n-k}. $

Sum of product of two combinations

Number of subsets $S \subset A_1 \cup A_2 \cup ... A_n$ where $|S \cap A_i| = a_i$?

An approximation of combinatorials using the geometric mean?

Prove binomial coefficient

What is the number of $6$ digit positive integers whose sum of the digits is at least $52$?

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