List questions from binomial-coefficients

Published on 16 Apr 2026 - 3:37

43

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In how many ways can a given process occur

Published on 11 Apr 2026 - 3:52

866

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Why does the multinomial coefficient count permutations but the binomial coefficient count combinations?

Published on 26 Mar 2026 - 4:49

140

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Combinatorially proving $F_{n} = \sum_{i=0}^{\left\lfloor n/2 \right\rfloor}\binom{n-i}{i}$, where $F_n$ is the $n$-th Fibonacci number

Published on 17 Apr 2026 - 7:36

58

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How to get this lower bound for $C(m^2,m-1)$?

Published on 13 Apr 2026 - 19:49

192

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Partial sum of alternating series involving binomials

Published on 14 Apr 2026 - 3:35

127

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Binomial Coefficient through multiplication only

Published on 13 Apr 2026 - 22:20

215

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Series of polynomials very nearly follows binomial coefficients but doesn't quite

Published on 25 Mar 2026 - 22:06

65

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The limit of a Nasty Summation

Published on 14 Apr 2026 - 17:31

162

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How to prove that $\sum_{k=0}^n (-1)^k k^p \binom{n}{k}$ is non-zero for p>1

Published on 15 Apr 2026 - 15:32

85

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Explanation of $\sum_{k}[x^k]f(x)g(y)^k=f(g(y))$

Published on 16 Apr 2026 - 15:46

123

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Is there a $q$-analog for the product of binomial coefficients?

Published on 14 Apr 2026 - 23:30

186

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Conjecture: Shallow diagonals in Pascal's triangle form polynomials whose roots are all real, distinct, and in $(-2,2)$.

Published on 16 Apr 2026 - 1:35

87

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Convergence of a weighted alternating binomial series

Published on 13 Apr 2026 - 22:43

118

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Find the value of $T+2\sqrt3S$

Published on 16 Apr 2026 - 12:03

List Question

Find the expected number of hours all 512 people suffer

In how many ways can a given process occur

Why does the multinomial coefficient count permutations but the binomial coefficient count combinations?

Combinatorially proving $F_{n} = \sum_{i=0}^{\left\lfloor n/2 \right\rfloor}\binom{n-i}{i}$, where $F_n$ is the $n$-th Fibonacci number

How to get this lower bound for $C(m^2,m-1)$?

Partial sum of alternating series involving binomials

Binomial Coefficient through multiplication only

Series of polynomials very nearly follows binomial coefficients but doesn't quite

The limit of a Nasty Summation

How to prove that $\sum_{k=0}^n (-1)^k k^p \binom{n}{k}$ is non-zero for p>1

Explanation of $\sum_{k}[x^k]f(x)g(y)^k=f(g(y))$

Is there a $q$-analog for the product of binomial coefficients?

Conjecture: Shallow diagonals in Pascal's triangle form polynomials whose roots are all real, distinct, and in $(-2,2)$.

Convergence of a weighted alternating binomial series

Find the value of $T+2\sqrt3S$

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