Rule of Sum and the Inclusion-Exclusion Principle
Rule of Sum and the Inclusion-Exclusion Principle
If there are ways of getting a result and ways to get a result , then the number of ways of getting or is , as long as the results and do not overlap.
n(A)
A
n(B)
B
A
B
n(A)+n(B)
A
B
To get the right number when there is overlap, think of the possible results and as sets. Then the number of ways to get an element from or is . This is called the principle of inclusion-exclusion.
A
B
A
B
n(A⋃B)=n(A)+n(B)-n(A⋂B)