Question

Let , and be sets. Prove formally that | ∪ ∪ | = || + || + || − | ∩ | − | ∩ | − | ∩ | + | ∩ ∩ |

score 76 · Answer 1 · 2026-04-15 19:14:07

76

Views

Let , and be sets. Prove formally that | ∪ ∪ | = || + || + || − | ∩ | − | ∩ | − | ∩ | + | ∩ ∩ |

Published on 15 Apr 2026 - 19:14

score 113 · Answer 2 · 2026-04-09 19:09:21

113

Views

Explanation of counting by Inclusion Exclusion

Published on 09 Apr 2026 - 19:09

score 126 · Answer 3 · 2026-04-12 19:43:10

126

Views

Letters and Envelops problem

Published on 12 Apr 2026 - 19:43

score 61 · Answer 4 · 2026-04-14 20:42:17

61

Views

How many ways are there to divide n dancers into dance circles where in each circle num of dancers >=2?

Published on 14 Apr 2026 - 20:42

score 610 · Answer 5 · 2026-05-01 03:42:18

610

Views

Seating Arrangement with Derangement

Published on 01 May 2026 - 3:42

score 592 · Answer 6 · 2026-04-16 10:00:29

592

Views

Prove that $(1-x)^n \leq 1 -xn+\frac{n(n-1)}{2}x^2$ when $0\leq x\leq 1$ and $n\geq2$

Published on 16 Apr 2026 - 10:00

score 236 · Answer 7 · 2026-04-14 03:28:53

236

Views

Number of one-one function from sets $A$ to $B$.

Published on 14 Apr 2026 - 3:28

score 31 · Answer 8 · 2026-04-10 04:01:33

31

Views

Inclusion exclusion principle counting

Published on 10 Apr 2026 - 4:01

score 395 · Answer 9 · 2026-04-15 16:49:30

395

Views

Derangements $p$ of $1,2,\dots,n,n+1$ such that $n+1$ doesn't go to $n$

Published on 15 Apr 2026 - 16:49

score 136 · Answer 10 · 2026-04-11 12:44:55

136

Views

A Question on the Inclusion-Exclusion Principle in Probability Theory

Published on 11 Apr 2026 - 12:44

score 40 · Answer 11 · 2026-04-16 04:53:17

Given $a_1, a_2, \cdots, a_N$ such that $a_1+a_2+\cdots +a_N = S$ for some given $S$, find the number of ways such that someone is $\geq T$.

score 2.2k · Answer 12 · 2026-04-15 22:13:01

2.2k

Views

Number of ways of coloring n objects which are laid in a row with k colors such that the adjacent objects are of different colors

Published on 15 Apr 2026 - 22:13

score 851 · Answer 13 · 2026-04-14 16:07:49

851

Views

In how many ways can letters in a word CALCULUS be rearranged so that no two identical letters are adjacent?

Published on 14 Apr 2026 - 16:07

score 268 · Answer 14 · 2026-04-15 05:52:04

268

Views

What is the probability that no cup is on a saucer of the same colour?

Published on 15 Apr 2026 - 5:52

score 3k · Answer 15 · 2026-04-12 13:14:16

3k

Views

Envelope Question: Five letters addressed to individuals 1-5 are randomly placed in five addressed envelopes, one letter in each envelope.

Published on 12 Apr 2026 - 13:14

List Question

Let , and be sets. Prove formally that | ∪ ∪ | = || + || + || − | ∩ | − | ∩ | − | ∩ | + | ∩ ∩ |

Explanation of counting by Inclusion Exclusion

Letters and Envelops problem

How many ways are there to divide n dancers into dance circles where in each circle num of dancers >=2?

Seating Arrangement with Derangement

Prove that $(1-x)^n \leq 1 -xn+\frac{n(n-1)}{2}x^2$ when $0\leq x\leq 1$ and $n\geq2$

Number of one-one function from sets $A$ to $B$.

Inclusion exclusion principle counting

Derangements $p$ of $1,2,\dots,n,n+1$ such that $n+1$ doesn't go to $n$

A Question on the Inclusion-Exclusion Principle in Probability Theory

Given $a_1, a_2, \cdots, a_N$ such that $a_1+a_2+\cdots +a_N = S$ for some given $S$, find the number of ways such that someone is $\geq T$.

Number of ways of coloring n objects which are laid in a row with k colors such that the adjacent objects are of different colors

In how many ways can letters in a word CALCULUS be rearranged so that no two identical letters are adjacent?

What is the probability that no cup is on a saucer of the same colour?

Envelope Question: Five letters addressed to individuals 1-5 are randomly placed in five addressed envelopes, one letter in each envelope.

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