Combination with Repetition

When items are chosen from a set and repetition is allowed, the number of ways to select them changes dramatically — a single type can be picked multiple times. This is the idea behind combinations with repetition, often called "multichoose." For example, selecting 3 scoops of ice cream from 5 flavours, where you can repeat flavours, is a problem of this kind. The formula for the number of such selections is $\binom{n + r - 1} …