Concept
How many costume choices are possible when a child can select up to three accessories?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"Okay, that’s overkill. A kid only has two hands, after all, so handling nine accessories would be a dextrous challenge. Let’s say instead that a child can choose up to three accessories (but must have at least one). Now how many costume choices are there? Now it’s 4 × 5 × ((9 choose 1) + (9 choose 2) + (9 choose 3)), which is equal to 4 × 5 × (9 + 36 + 84), or 2,580 possible costumes."
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