List questions from binomial-coefficients

Published on 11 Apr 2026 - 1:59

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Why does Pascal's Triangle (mod 2) encode the Fermat primes?

Published on 16 Apr 2026 - 7:55

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approximation of a constant raised to a power that is less than one

Published on 10 Apr 2026 - 23:14

88

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Explicit distribution of B which has conditioned binomial distribution

Published on 09 Apr 2026 - 20:39

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Alternating sum of binomial of coefficients up to $\binom{n}{r}$

Published on 14 Apr 2026 - 12:59

223

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A purely combinatorial proof that $\binom{m+n}{n}$ divides $\binom{2n}{n}\cdot \binom{2m}{m}$

Published on 16 Apr 2026 - 14:22

200

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Ramanujan's Proof for Morley's Hypergeometric Identity

Published on 10 Apr 2026 - 18:12

54

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Understanding the meaning of the notation $\binom{n+m}{n,m}$

Published on 14 Apr 2026 - 4:43

92

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Limit of $\sum_{n=1}^k\sum_{k=k_1+\dotsb+k_n}\frac{1}{n!}\frac{1}{k_1\cdots k_n}$

Published on 15 Apr 2026 - 0:10

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What is the probability that, having $N$ numbered balls and performing $n$ extractions, I have $n−m$ non-repeated balls?

Published on 14 Apr 2026 - 21:15

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Urn with replacement, 3 colours, drawing all colours

Published on 13 Apr 2026 - 23:22

326

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Some curious binomial coefficient identities

Published on 14 Apr 2026 - 7:32

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Find remainder in binomial expression

Published on 13 Apr 2026 - 3:17

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Prove by induction that $\sum_{r=0}^{n}\binom nr =2^k$

Published on 10 Apr 2026 - 23:57

404

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Prove $\binom{2p+1}{p}\equiv2$ mod $p$ when $p$ is any prime.

Published on 17 Apr 2026 - 9:45

List Question

Probability of selecting 2 defective bulbs

Why does Pascal's Triangle (mod 2) encode the Fermat primes?

approximation of a constant raised to a power that is less than one

Explicit distribution of B which has conditioned binomial distribution

Alternating sum of binomial of coefficients up to $\binom{n}{r}$

A purely combinatorial proof that $\binom{m+n}{n}$ divides $\binom{2n}{n}\cdot \binom{2m}{m}$

Ramanujan's Proof for Morley's Hypergeometric Identity

Understanding the meaning of the notation $\binom{n+m}{n,m}$

Limit of $\sum_{n=1}^k\sum_{k=k_1+\dotsb+k_n}\frac{1}{n!}\frac{1}{k_1\cdots k_n}$

What is the probability that, having $N$ numbered balls and performing $n$ extractions, I have $n−m$ non-repeated balls?

Urn with replacement, 3 colours, drawing all colours

Some curious binomial coefficient identities

Find remainder in binomial expression

Prove by induction that $\sum_{r=0}^{n}\binom nr =2^k$

Prove $\binom{2p+1}{p}\equiv2$ mod $p$ when $p$ is any prime.

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