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A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to purchase 3 scoops of ice-cream, in how many ways can one make that purchase?

1. 4
2. 20
3. 24
4. 48

Correct answer: 20

Solution

The problem can be solved using the stars and bars combinatorial method, where the 3 scoops (stars) are distributed among 4 flavors (bins). The formula for this is given by the combination of (n+k-1) choose (k-1), where n is the number of scoops and k is the number of flavors, resulting in 20 ways.

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