Probability & Combinatorics
Advanced

Inclusion-Exclusion (3 sets)

Counts the union of overlapping sets without double counting.

Formula

∣A∪B∪C∣=∣A∣+∣B∣+∣C∣−∣A∩B∣−∣A∩C∣−∣B∩C∣+∣A∩B∩C∣|A\cup B\cup C| = |A|+|B|+|C|-|A\cap B|-|A\cap C|-|B\cap C|+|A\cap B\cap C|

Variables

A,B,CSets

Example

Corrects for all overlaps systematically

Did You Know?

Generalizes to any number of sets with alternating signs.

countingsets