Question

The Matching Problem: Probability of At Least One Man Selecting His Own Hat

score 491 · Answer 1 · 2026-02-24 01:52:07

491

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The Matching Problem: Probability of At Least One Man Selecting His Own Hat

Published on 24 Feb 2026 - 1:52

score 82 · Answer 2 · 2026-02-24 01:53:51

82

Views

Solve the recurrence $ x_n = 4n(n-1) \cdot (x_{n-1} + 2 (n-1) x_{n-2})$ for $x_1 = 0$ and $x_2 = 16$

Published on 24 Feb 2026 - 1:53

score 261 · Answer 3 · 2026-02-24 01:53:52

261

Views

In how many ways can $n$ letters can be placed in $m$ $(m>n)$ addressed envelopes, such that no letter is put in the correct envelope?

Published on 24 Feb 2026 - 1:53

score 248 · Answer 4 · 2026-02-24 01:46:07

248

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Permutations with matching

Published on 24 Feb 2026 - 1:46

score 159 · Answer 5 · 2026-02-24 01:53:41

159

Views

Find the number of failed Secret Santa games for N people

Published on 24 Feb 2026 - 1:53

score 33 · Answer 6 · 2026-02-24 01:49:44

33

Views

Probability that no student gets his own paper back

Published on 24 Feb 2026 - 1:49

score 35 · Answer 7 · 2026-02-24 01:55:14

35

Views

What is the probability that at least one suitcase ends up with its original traveller?

Published on 24 Feb 2026 - 1:55

score 432 · Answer 8 · 2026-02-24 01:49:09

432

Views

A little help with Derangements

Published on 24 Feb 2026 - 1:49

score 70 · Answer 9 · 2026-02-24 01:48:47

70

Views

Question about a step in a derangement proof

Published on 24 Feb 2026 - 1:48

score 40 · Answer 10 · 2026-02-24 01:48:21

40

Views

Derangements, finding best possible $k$

Published on 24 Feb 2026 - 1:48

score 230 · Answer 11 · 2026-02-24 01:53:40

230

Views

Counting permutations $\pi \in S_n$ such that $\pi(i) \neq i$ and $\pi(i) - k \not\equiv i \bmod n$.

Published on 24 Feb 2026 - 1:53

score 125 · Answer 12 · 2026-02-24 01:53:59

125

Views

Colouring an $n \times n$ grid s.t. no row or column contains the same colour

Published on 24 Feb 2026 - 1:53

score 692 · Answer 13 · 2026-02-24 01:54:40

692

Views

Number of ways to place $n$ rooks on $n$ by $n$ board such that they don't hit each other. But someone has cut out squares of one of diagonals.

Published on 24 Feb 2026 - 1:54

score 217 · Answer 14 · 2026-02-24 01:52:08

217

Views

Why is the probably four all receive the wrong dish not $\frac{1}{2}$?

Published on 24 Feb 2026 - 1:52

score 37 · Answer 15 · 2026-02-24 01:51:04

37

Views

Numbered runners finishing with their shirt numbers

Published on 24 Feb 2026 - 1:51

List Question

The Matching Problem: Probability of At Least One Man Selecting His Own Hat

Solve the recurrence $ x_n = 4n(n-1) \cdot (x_{n-1} + 2 (n-1) x_{n-2})$ for $x_1 = 0$ and $x_2 = 16$

In how many ways can $n$ letters can be placed in $m$ $(m>n)$ addressed envelopes, such that no letter is put in the correct envelope?

Permutations with matching

Find the number of failed Secret Santa games for N people

Probability that no student gets his own paper back

What is the probability that at least one suitcase ends up with its original traveller?

A little help with Derangements

Question about a step in a derangement proof

Derangements, finding best possible $k$

Counting permutations $\pi \in S_n$ such that $\pi(i) \neq i$ and $\pi(i) - k \not\equiv i \bmod n$.

Colouring an $n \times n$ grid s.t. no row or column contains the same colour

Number of ways to place $n$ rooks on $n$ by $n$ board such that they don't hit each other. But someone has cut out squares of one of diagonals.

Why is the probably four all receive the wrong dish not $\frac{1}{2}$?

Numbered runners finishing with their shirt numbers

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