An ice-cream parlour offers 15 different flavours of ice-cream. An ice-cream sundae contains 5 scoops of ice-cream. An ice-cream parlour offers 15 different flavours of ice-cream. An ice-cream sundae contains 5 scoops of ice-cream. Suppose someone selects the five scoops of a sundae at random (repetitions allowed). What is the probability that the ice-cream sundae contains exactly 2 scoops of vanilla ice-cream? I would calculate the number of different ice cream sundaes as following: $15^5$$=$$759375$. Then i would calculate the possible ways of ice cream sundays with two vanilla scoops and divide it by $15^5$. But i do not know how to calculate possibilities of choosing exactly two scoops of vanilla ice-cream. I am really stuck and would appreciate any help or hint. My guess what have been $15*1*14*14*14$ but it seems to be wrong.

Think of the possible choices for each scoop. $$ 1 * 1 * 14 * 14 * 14$$

Since we want exactly 2 scoops of vanilla.

Now think of how many ways we can get this order.

We multiply by $\frac{5!}{2!3!}$ because there are 5 scoops made up of 2 vanilla and 3 non-vanilla.

Solution = 27440 possibilities.