An ice cream store offers 29 different flavors of ice cream. How many triple-scoop ice cream cones are possible if each scoop must be a different flavor and the flavors can be in any order?
A) 21924
B) 24389
C) 3654
D) 87
E) 754

Question

Quizplus · Accepted Answer

The number of ways to choose 3 different flavors from 29, where the order matters, is calculated using permutations: $P(29, 3) = \frac{29!}{(29-3)!} = \frac{29!}{26!} = 29 \times 28 \times 27 = 21924$. However, since the order of scoops on the cone does not matter, we actually need to use combinations: $C(29, 3) = \frac{29!}{3!(29-3)!} = \frac{29!}{3!26!} = \frac{29 \times 28 \times 27}{3 \times 2 \times 1} = 3654$.

An Ice Cream Store Offers 29 Different Flavors of Ice