Question

Baskin-Robbins offers 31 different flavors of ice cream. One of its items is a bowl consisting of three scoops of ice cream, each a different flavor. How many such bowls are possible?

Answer 1

The answer is the number of subsets with cardinality 3 that we can extract from a set with cardinality 31.

The answer is the binomial coefficient

$\displaystyle\binom{n}{k}=\dfrac{n!}{k!(n-k)!}$

Where the factorial is defined as

$n!=n(n-1)(n-2)(n-3)\ldots 3\cdot 2$

So, your answer is

$\displaystyle\binom{31}{3}=\dfrac{31!}{3!\;28!}=\dfrac{31\cdot 30\cdot 29\cdot 28\ldots 2}{3\cdot 2\cdot 28\ldots 2}=\dfrac{31\cdot 30\cdot 29}{3\cdot 2}=31\cdot29\cdot5=4495$