A shop has 4 distinct flavors of ice-cream. One can purchase any number of…

Answer: 20

Explanation: We need the number of ways to choose 3 scoops from 4 distinct flavors when repetition is allowed and order does not matter. This is the number of multisets of size 3 from 4 types.

• Use the combinations with repetition formula (stars and bars): the number is C(n + k - 1, k), where n = number of flavors and k = number of scoops.

• Here n = 4 and k = 3, so the count is C(4 + 3 - 1, 3) = C(6, 3).

• Compute C(6,3) = 6*5*4 / (3*2*1) = 120 / 6 = 20.

Quick notes on the incorrect numerical choices:

• The value 4 counts only the cases where all three scoops are the same flavor (one per flavor).

• The value 24 is 4P3, counting ordered selections of three distinct flavors with no repetition; that assumes order matters and repeats are forbidden, which does not match the problem.

• The value 48 does not follow from the correct model and likely comes from mixing different incorrect assumptions about order and repetition.