Question

In how many ways $n$ distinct objects can be distributed to $k$ identical bins if bins may be left empty?

score 410 · Answer 1 · 2020-10-18 05:44:47

410

Views

In how many ways $n$ distinct objects can be distributed to $k$ identical bins if bins may be left empty?

Published on 18 Oct 2020 - 5:44

score 454 · Answer 2 · 2026-03-29 16:34:38

454

Views

Proof by induction that Catalan number $C_n$ is less or equal to $n!$

Published on 29 Mar 2026 - 16:34

score 64 · Answer 3 · 2020-10-18 23:52:15

64

Views

Unique representation: $a!\cdot b!\cdot c!=m!\cdot n!\cdot p!$

Published on 18 Oct 2020 - 23:52

score 59 · Answer 4 · 2020-10-20 13:51:48

59

Views

Dividing a matrix to the power of r

Published on 20 Oct 2020 - 13:51

score 60 · Answer 5 · 2020-10-21 14:37:51

60

Views

A way to solve equations of the form $(\frac{n}{a})! = b$?

Published on 21 Oct 2020 - 14:37

score 108 · Answer 6 · 2026-04-04 15:21:53

108

Views

Summation of $n$th partial products of the square of even numbers diverges, but for odd numbers they converge in this series I'm looking at. Why?

Published on 04 Apr 2026 - 15:21

score 35 · Answer 7 · 2020-10-21 19:41:58

35

Views

I don't know if my answer is correct, can you confirm? How to prove?

Published on 21 Oct 2020 - 19:41

score 462 · Answer 8 · 2020-10-22 07:20:45

462

Views

Which is larger $(101!)^{100}$ or $(100!)^{101}$

Published on 22 Oct 2020 - 7:20

score 413 · Answer 9 · 2020-10-23 04:25:06

413

Views

Prove that $18!+1$ is divisible by $19$ and $23$

Published on 23 Oct 2020 - 4:25

score 76 · Answer 10 · 2020-10-25 04:30:55

76

Views

Proof by induction $(2 n)! \geq n!^2$

Published on 25 Oct 2020 - 4:30

score 87 · Answer 11 · 2020-10-25 14:00:57

87

Views

Find the nature of $\sum_{n = 1}^\infty \frac{1! + 2! + \cdots + n!}{(n + 2)!}$

Published on 25 Oct 2020 - 14:00

score 67 · Answer 12 · 2026-03-25 12:44:14

67

Views

Name of the formula for divisibility of factorials

Published on 25 Mar 2026 - 12:44

score 974 · Answer 13 · 2026-04-12 00:39:31

974

Views

In how many ways can nine students be divided into three labeled teams (A, B, C) of three people?

Published on 12 Apr 2026 - 0:39

score 80 · Answer 14 · 2020-10-25 16:53:36

80

Views

Find the nature of $\sum_{n = 1}^\infty \frac{(2n - 1)!!}{(2n)!! (2n + 1)}$

Published on 25 Oct 2020 - 16:53

score 41 · Answer 15 · 2020-10-25 22:11:19

41

Views

Proving $\frac{(-1)^n(2n)!}{(n!)^2}+2\sum_{i=0}^{n-1}\frac{(-1)^i(2n)!}{i!(2n-i)!} = 0$ for positive integer $n$

Published on 25 Oct 2020 - 22:11

List Question

In how many ways $n$ distinct objects can be distributed to $k$ identical bins if bins may be left empty?

Proof by induction that Catalan number $C_n$ is less or equal to $n!$

Unique representation: $a!\cdot b!\cdot c!=m!\cdot n!\cdot p!$

Dividing a matrix to the power of r

A way to solve equations of the form $(\frac{n}{a})! = b$?

Summation of $n$th partial products of the square of even numbers diverges, but for odd numbers they converge in this series I'm looking at. Why?

I don't know if my answer is correct, can you confirm? How to prove?

Which is larger $(101!)^{100}$ or $(100!)^{101}$

Prove that $18!+1$ is divisible by $19$ and $23$

Proof by induction $(2 n)! \geq n!^2$

Find the nature of $\sum_{n = 1}^\infty \frac{1! + 2! + \cdots + n!}{(n + 2)!}$

Name of the formula for divisibility of factorials

In how many ways can nine students be divided into three labeled teams (A, B, C) of three people?

Find the nature of $\sum_{n = 1}^\infty \frac{(2n - 1)!!}{(2n)!! (2n + 1)}$

Proving $\frac{(-1)^n(2n)!}{(n!)^2}+2\sum_{i=0}^{n-1}\frac{(-1)^i(2n)!}{i!(2n-i)!} = 0$ for positive integer $n$

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