List questions from binomial-coefficients

Published on 13 Apr 2026 - 23:02

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What is the limit of this sequence created using Pascal's triangle?

Published on 12 Apr 2026 - 21:34

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Number of ways in which 3 people can throw a normal die to have a total score of 11

Published on 25 Mar 2026 - 23:42

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Calculate $\sum_{j=1}^{n}\sum_{i=1}^{j}j\cdot i$ using binomial coefficients.

Published on 16 Apr 2026 - 6:10

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Prove that $\sum_{r=0}^k {{n}\choose{r}} < \frac{n^n}{k^k (n-k)^{n-k}}$

Published on 16 Apr 2026 - 10:57

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Use combinatorial argument to prove the following identites:

Published on 15 Apr 2026 - 14:24

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What does "the sum of every third element in the $n$-th row of Pascal's triangle" mean?

Published on 13 Apr 2026 - 22:33

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Combinatorial Proof - Equating binomials

Published on 16 Apr 2026 - 20:42

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How do I add the terms in the binomial expansion of $(100+2)^6$?

Published on 11 Apr 2026 - 9:01

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Value of $\sum_{k=0}^{\ell} (-1)^k\binom{n}{k}k^p$

Published on 16 Apr 2026 - 13:19

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Binomial coefficient complex expression

Published on 10 Apr 2026 - 9:40

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Partial Binomial Sums

Published on 11 Apr 2026 - 13:56

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Probability notation two numbers stacked inside brackets

Published on 10 Apr 2026 - 8:39

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Binomial Coefficients and series

Published on 14 Apr 2026 - 3:53

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Evaluating $\frac{\sum_{i=0}^{100} \binom{k}{i} \binom{M-k}{100-i} \frac{k-i}{M-100}}{\binom{M}{100}}$

Published on 17 Apr 2026 - 5:28

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Solving inequality with partial sum of binomial coefficient

What is the limit of this sequence created using Pascal's triangle?

Number of ways in which 3 people can throw a normal die to have a total score of 11

Calculate $\sum_{j=1}^{n}\sum_{i=1}^{j}j\cdot i$ using binomial coefficients.

Prove that $\sum_{r=0}^k {{n}\choose{r}} < \frac{n^n}{k^k (n-k)^{n-k}}$

Use combinatorial argument to prove the following identites:

What does "the sum of every third element in the $n$-th row of Pascal's triangle" mean?

Combinatorial Proof - Equating binomials

How do I add the terms in the binomial expansion of $(100+2)^6$?

Value of $\sum_{k=0}^{\ell} (-1)^k\binom{n}{k}k^p$

Binomial coefficient complex expression

Partial Binomial Sums

Probability notation two numbers stacked inside brackets

Binomial Coefficients and series

Evaluating $\frac{\sum_{i=0}^{100} \binom{k}{i} \binom{M-k}{100-i} \frac{k-i}{M-100}}{\binom{M}{100}}$

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