Question

Bijection between the set of coin tosses with an equal number of $H$'s and $T$'s and the set where $H$'s and $T$'s are never equal

score 102 · Answer 1 · 2026-03-28 08:35:33

102

Views

Bijection between the set of coin tosses with an equal number of $H$'s and $T$'s and the set where $H$'s and $T$'s are never equal

Published on 28 Mar 2026 - 8:35

score 86 · Answer 2 · 2026-04-14 15:43:17

86

Views

When dividing binomial coefficients by $3$, why is remainder $1$ much more common than remainder $2$?

Published on 14 Apr 2026 - 15:43

score 83 · Answer 3 · 2026-04-12 15:35:03

83

Views

$\sum_{r=0}^n \binom{n}{r}2^{n-r}\binom{r}{[\frac{r}{2}]}$

Published on 12 Apr 2026 - 15:35

score 93 · Answer 4 · 2026-04-15 18:08:39

93

Views

Combinatorial proof for $n > k > 0$: $\sum_{j=0}^n {{k}\choose{j}} {{n-k}\choose{j}} = {{n}\choose{k}}$

Published on 15 Apr 2026 - 18:08

score 77 · Answer 5 · 2026-04-16 02:49:15

77

Views

Combinatorial proof for $n \in \mathbb{N}$: $\sum_{k=0}^n \sum_{j=0}^n {{k}\choose{j}} {{n-k}\choose{j}} = \sum_{m=0}^n {{n+1}\choose{2m+1}} $

Published on 16 Apr 2026 - 2:49

score 73 · Answer 6 · 2026-04-13 20:13:36

73

Views

Proving formula with binomial coefficients

Published on 13 Apr 2026 - 20:13

score 255 · Answer 7 · 2026-04-11 14:18:51

255

Views

Possible new formula for OEIS A191522

Published on 11 Apr 2026 - 14:18

score 48 · Answer 8 · 2026-04-14 19:21:41

48

Views

Showing the binomial identity of $\sum_{k=0}^{2n}\binom{2n}{k}=\sum_{k=0}^n \binom{2n}{k}+\sum_{k=1}^n \binom{2n}{n+k}$

Published on 14 Apr 2026 - 19:21

score 95 · Answer 9 · 2026-04-15 10:23:37

95

Views

Prove that $\sum_{k=n}^{5n} C_{k-1}^{n-1} (4/5)^{k-n}$ is equal to 1

Published on 15 Apr 2026 - 10:23

score 180 · Answer 10 · 2026-04-15 05:18:26

180

Views

Closed form for $\sum_{n=1}^\infty\binom{2n}{n}\zeta(m,n+1)x^n$

Published on 15 Apr 2026 - 5:18

score 85 · Answer 11 · 2026-04-12 21:24:17

85

Views

Using tricks to Maximize a Product of Binomial Coefficients $\binom{n}{x} \times \binom{n}{b - ax}$

Published on 12 Apr 2026 - 21:24

score 122 · Answer 12 · 2026-04-16 12:19:36

122

Views

Finding the cardinality of $\{(a, S) \mid a ∈ S, S ∈ P(A)\}$ for $A =\{1, 2, 3, \cdots , n\}$.

Published on 16 Apr 2026 - 12:19

score 106 · Answer 13 · 2026-04-14 12:56:40

106

Views

A simple question on binomial.(a Typo or not?)

Published on 14 Apr 2026 - 12:56

score 47 · Answer 14 · 2026-04-14 23:10:00

47

Views

Binomial form of $\frac{A(A+1) \cdots (A+n-2)}{(s+A-1)(s+A-2) \cdots (s+A-i+1)}$

Published on 14 Apr 2026 - 23:10

score 56 · Answer 15 · 2026-04-16 10:31:46

56

Views

Simplify $ \sum\limits_{i=0}^l{n\choose i}{m\choose l-i}$

Published on 16 Apr 2026 - 10:31

List Question

Bijection between the set of coin tosses with an equal number of $H$'s and $T$'s and the set where $H$'s and $T$'s are never equal

When dividing binomial coefficients by $3$, why is remainder $1$ much more common than remainder $2$?

$\sum_{r=0}^n \binom{n}{r}2^{n-r}\binom{r}{[\frac{r}{2}]}$

Combinatorial proof for $n > k > 0$: $\sum_{j=0}^n {{k}\choose{j}} {{n-k}\choose{j}} = {{n}\choose{k}}$

Combinatorial proof for $n \in \mathbb{N}$: $\sum_{k=0}^n \sum_{j=0}^n {{k}\choose{j}} {{n-k}\choose{j}} = \sum_{m=0}^n {{n+1}\choose{2m+1}} $

Proving formula with binomial coefficients

Possible new formula for OEIS A191522

Showing the binomial identity of $\sum_{k=0}^{2n}\binom{2n}{k}=\sum_{k=0}^n \binom{2n}{k}+\sum_{k=1}^n \binom{2n}{n+k}$

Prove that $\sum_{k=n}^{5n} C_{k-1}^{n-1} (4/5)^{k-n}$ is equal to 1

Closed form for $\sum_{n=1}^\infty\binom{2n}{n}\zeta(m,n+1)x^n$

Using tricks to Maximize a Product of Binomial Coefficients $\binom{n}{x} \times \binom{n}{b - ax}$

Finding the cardinality of $\{(a, S) \mid a ∈ S, S ∈ P(A)\}$ for $A =\{1, 2, 3, \cdots , n\}$.

A simple question on binomial.(a Typo or not?)

Binomial form of $\frac{A(A+1) \cdots (A+n-2)}{(s+A-1)(s+A-2) \cdots (s+A-i+1)}$

Simplify $ \sum\limits_{i=0}^l{n\choose i}{m\choose l-i}$

Trending Questions

Popular # Hahtags

Popular Questions