 # Rule of Sum and the Inclusion-Exclusion Principle

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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.

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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.

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Contributed by: George Beck (July 2018)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

The sum rule generalizes when there are more than two kinds of results, giving ,

as long as all the pairwise intersections , , , are empty.

If there are overlaps, the right-hand side of the formula is an alternating sum. For example, here is the formula for three sets: .

Reference

 Wikipedia. "Rule of Sum." (Jun 4, 2018) en.wikipedia.org/wiki/Rule_of_sum.

## Permanent Citation

George Beck

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