List questions from binomial-coefficients

Published on 28 Mar 2026 - 6:40

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Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$

Published on 20 Mar 2014 - 19:09

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How do you prove ${n \choose k}$ is maximum when $k$ is $ \lceil \tfrac n2 \rceil$ or $ \lfloor \tfrac n2\rfloor $?

Published on 23 Mar 2014 - 6:07

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In a lottery of $90$ numbers a man adds extra $1,2,3$

Published on 23 Mar 2014 - 10:55

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find the the variable that maximizes a function

Published on 24 Mar 2014 - 7:43

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Function returning number of subsets of size $k$ of a set of size $n$.

Published on 29 Mar 2026 - 20:51

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Evaluate the summation involving binomials.

Published on 24 Mar 2014 - 16:15

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Binomial Distribution - independence

Published on 24 Mar 2014 - 20:37

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show that these two equation holds by binomial theorem

Published on 28 Mar 2026 - 5:01

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binomial coefficient divisibility properties

Published on 25 Mar 2014 - 9:56

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Does this really converge to 1/e? (Massaging a sum)

Published on 29 Mar 2026 - 20:49

266

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MCA entrance question

Published on 31 Mar 2026 - 15:10

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How to calculate this sum: $\sum_{k=1}^{n} \frac{k}{n^k} \binom nk$

Published on 27 Mar 2026 - 13:25

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Calculate sum with binomial coefficients: $\sum_{k=0}^{n} \frac{1}{k+1} \binom nk x^{k+1}$

Published on 27 Mar 2026 - 13:25

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What is the value of $1 + {{}^nP_2}/2 +{{}^nP_3}/3 + ~........... ~ {}^nP_n/n $

Published on 28 Mar 2014 - 7:36

List Question

Prove $\sum\limits_{r=0}^{2n} r \binom{2n}{r}^2 = 2n \binom{4n-1}{2n}$

Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$

How do you prove ${n \choose k}$ is maximum when $k$ is $ \lceil \tfrac n2 \rceil$ or $ \lfloor \tfrac n2\rfloor $?

In a lottery of $90$ numbers a man adds extra $1,2,3$

find the the variable that maximizes a function

Function returning number of subsets of size $k$ of a set of size $n$.

Evaluate the summation involving binomials.

Binomial Distribution - independence

show that these two equation holds by binomial theorem

binomial coefficient divisibility properties

Does this really converge to 1/e? (Massaging a sum)

MCA entrance question

How to calculate this sum: $\sum_{k=1}^{n} \frac{k}{n^k} \binom nk$

Calculate sum with binomial coefficients: $\sum_{k=0}^{n} \frac{1}{k+1} \binom nk x^{k+1}$

What is the value of $1 + {{}^nP_2}/2 +{{}^nP_3}/3 + ~........... ~ {}^nP_n/n $

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