Question

How many $01$ or $10$ substrings are there, on average, in a random $n$-bit string containing $k$ ones.

score 61 · Answer 1 · 2022-02-02 01:04:06

61

Views

How many $01$ or $10$ substrings are there, on average, in a random $n$-bit string containing $k$ ones.

Published on 02 Feb 2022 - 1:04

score 152 · Answer 2 · 2022-02-03 01:45:19

152

Views

Examples of proofs that are easiest by double counting.

Published on 03 Feb 2022 - 1:45

score 80 · Answer 3 · 2022-02-09 02:57:04

80

Views

Help finding a proof of an identity $\sum_{k=0}^{n}(-1)^{k}\binom{j}{k}$

Published on 09 Feb 2022 - 2:57

score 284 · Answer 4 · 2022-02-10 23:43:36

284

Views

Combinatorial proof for $\sum_{i=0}^{k} i {k \choose i} {{n-k}\choose{k-i}} = k{{n-1}\choose{k-1}}$

Published on 10 Feb 2022 - 23:43

score 68 · Answer 5 · 2022-02-16 11:43:08

68

Views

Combinatorial proof of $\binom{n+2}{3} = 1 \cdot n + 2 \cdot (n-1) + 3 \cdot (n-2) + \cdots + n \cdot 1$

Published on 16 Feb 2022 - 11:43

score 82 · Answer 6 · 2026-03-30 13:37:05

82

Views

Counting exactly 5 spades from 6 cards

Published on 30 Mar 2026 - 13:37

score 117 · Answer 7 · 2022-02-21 13:22:29

117

Views

${ n \choose k}={ n-1 \choose k-1}+{ n-2 \choose k-1}+{ n-3 \choose k-1}+...+{ k-1 \choose k-1}$

Published on 21 Feb 2022 - 13:22

score 95 · Answer 8 · 2026-03-30 03:37:54

95

Views

prove that $\sum_{k=0}^{n}S(n,k)(x)_k=x^n$

Published on 30 Mar 2026 - 3:37

score 39 · Answer 9 · 2022-02-25 06:57:55

39

Views

Proving the identity $\sum_{i=0}^n{n + i \choose i}\frac{1}{2^i} = 2^n$ combinatorially

Published on 25 Feb 2022 - 6:57

score 226 · Answer 10 · 2022-02-26 18:51:17

226

Views

Alternative way of writing the stars and bars formula where each bar is associated with at least one star.

Published on 26 Feb 2022 - 18:51

score 68 · Answer 11 · 2022-02-27 17:32:42

68

Views

Ballot problem but the probability that candidate B is ahead of candidate A

Published on 27 Feb 2022 - 17:32

score 80 · Answer 12 · 2022-02-27 19:20:57

80

Views

How can I prove $\Sigma ^{n-1} _{i=1} i = (^n _2)$? (n≥2)

Published on 27 Feb 2022 - 19:20

score 122 · Answer 13 · 2026-03-30 06:10:52

122

Views

A giant cube is made of $n^3$ small cubes so that its dimensions are $nxnxn$. How many cubes of any size can be made of small cubes in the giant cube?

Published on 30 Mar 2026 - 6:10

score 99 · Answer 14 · 2022-03-04 07:03:31

99

Views

Elements of combinatorial analysis

Published on 04 Mar 2022 - 7:03

score 142 · Answer 15 · 2022-03-06 13:55:00

142

Views

Proving that ${n \choose 1} - 2{n \choose 2} + 3{n \choose 3} + \dots + (-1)^{n - 1}n{n \choose n} = 0$

Published on 06 Mar 2022 - 13:55

List Question

How many $01$ or $10$ substrings are there, on average, in a random $n$-bit string containing $k$ ones.

Examples of proofs that are easiest by double counting.

Help finding a proof of an identity $\sum_{k=0}^{n}(-1)^{k}\binom{j}{k}$

Combinatorial proof for $\sum_{i=0}^{k} i {k \choose i} {{n-k}\choose{k-i}} = k{{n-1}\choose{k-1}}$

Combinatorial proof of $\binom{n+2}{3} = 1 \cdot n + 2 \cdot (n-1) + 3 \cdot (n-2) + \cdots + n \cdot 1$

Counting exactly 5 spades from 6 cards

${ n \choose k}={ n-1 \choose k-1}+{ n-2 \choose k-1}+{ n-3 \choose k-1}+...+{ k-1 \choose k-1}$

prove that $\sum_{k=0}^{n}S(n,k)(x)_k=x^n$

Proving the identity $\sum_{i=0}^n{n + i \choose i}\frac{1}{2^i} = 2^n$ combinatorially

Alternative way of writing the stars and bars formula where each bar is associated with at least one star.

Ballot problem but the probability that candidate B is ahead of candidate A

How can I prove $\Sigma ^{n-1} _{i=1} i = (^n _2)$? (n≥2)

A giant cube is made of $n^3$ small cubes so that its dimensions are $nxnxn$. How many cubes of any size can be made of small cubes in the giant cube?

Elements of combinatorial analysis

Proving that ${n \choose 1} - 2{n \choose 2} + 3{n \choose 3} + \dots + (-1)^{n - 1}n{n \choose n} = 0$

Trending Questions

Popular # Hahtags

Popular Questions