What is the Inclusion-Exclusion Principle?

What is the Inclusion-Exclusion Principle?

The inclusion-exclusion principle is a combinatoric way of computing the size of multiple intersecting sets or the probability of complex overlapping events....

Generalised Inclusion-Exclusion over Set:

For 2 Intersecting Set A and B: For 3 Intersecting Set A, B and C: Inclusion Exclusion Principle on 3 overlapping sets.For N Intersecting Sets: From above formulations we can clearly observe a pattern where odd combinations of set gets added while even Combination of Set gets Subtracted. This can be used to generalize our idea of inclusion and exclusion over a wide range of sets where: Get All combinations of sets i.e. all (2^N-1) Add the ones which have odd number of sets.Subtract the ones which have even number of sets....

Use Case of Inclusion Exclusion Principle:

1. Number of Divisors with certain conditions:...

Practice Problems on Inclusion Exclusion principle:

Prefix Sum of Matrix (Or 2D Array)Count ways to create string of size N with given restrictionsCount ways of selecting X red balls and Y blue ballsCount ways choosing K balls from any given A boxesCount number of ways in which following people can be arrangedCount ways to choose Triplets of Pairs such that either first or second values are distinct...