A class has 30 students. 18 are in the math club, 15 are in the coding club, 8 are in both. How many students are in at least one club?
If you add 18 + 15 = 33, you count the 8 overlapping students twice. Correct count: 18 + 15 - 8 = 25 students.
Inclusion-exclusion removes the double-count. This extends to three or more sets with alternating signs.