A catering service offers 12 appetizers, 9 main courses, and 6 desserts. A customer is to select 5 appetizers, 3 main courses, and 4 desserts for a banquet. In how many ways can this be done?
2026-03-28 17:39:32.1774719572
Permutations, combinations, and the multiplication principle for counting
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I am still new to this topic, but I think it is solved by
Appetizers = $ 12\choose{5}$ = 792
Main course = $ 9\choose{3}$ = 84
Dessert = $ 6\choose{4}$ = 15
I hope this helps I am not sure if I am right.
Based on the comment below, you multiply them. I think it is because of multiplication rule "and" .
So the answer becomes 792 * 84 * 15 = 997,920.