Questions tagged [inclusion-exclusion]

The inclusion-exclusion principle states that the number of elements in the union of two given sets is the sum of the number of elements in each set, minus the number of elements that are in both sets.

878 questions
22 views

what do we call the events that one of them is subset of the other

how to describe the relationship (exclusive, inclusive,.. etc) between two events that one is a subset of the other? example: if 'event 1' happened then 100% 'event 2' have happened.
44 views

Number of integers $n$ between 1 and 1000 such that the HCF of $n$ and $36$ is 1

How many integers $n$ are there such that $1< n < 1000$ and the highest common factor of $n$ and $36$ is $1$? I have tried counting the prime numbers up to $1000$ using the prime-counting ...
81 views

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

A tea set comprises four cups and saucers in four distinct colours. If the cups are placed at random on the saucers, what is the probability that no cup is on a saucer of the same colour? MY ATTEMPT ...
25 views

How many labeled rooted trees are there on 12 nodes where no node has exactly 4 children?

Problem: How many labeled rooted trees are there on 12 nodes where no node has exactly 4 children. I thought to use the principle of inclusion-exclusion. Let $N_i$ be the set of rooted labeled ...
$$S=\sum_{A+B+C+D=N}{N\choose A,B,C,D},$$ where $A \geq a$, $B \geq b$, $C \geq c$, $D \geq d$ Is there a way to find $S$ using inclusion-exclusion?