Exercise 230Combinatorics › Counting principlesHigh schoolAdded 3 Nov 2026

The sum rule

#sum rule#addition principle#disjoint cases

Statement

A menu offers $4$ starters, $6$ main courses, and $3$ desserts. How many ways are there to choose exactly one item (of any type)?

Hint

The three sets are disjoint, so add the sizes.

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Disjoint sets. The starter, main, and dessert options are pairwise disjoint sets.

Sum rule. Number of choices $=4+6+3=13$ .

Conclusion. There are $13$ ways to choose exactly one item.