Ice-cream tubs with repetition

Problem

An ice-cream seller has $20$ flavours. How many tubs of $3$ scoops can be made if the scoops may repeat?

Solution

The order of the scoops in the tub does not matter and the flavours may repeat: these are combinations with repetition of $n=20$ objects taken in groups of $k=3$. The formula is $\binom{n+k-1}{k}$: $\binom{20+3-1}{3} = \binom{22}{3} = \frac{22\cdot 21\cdot 20}{3!} = \boxed{1540}$

Links

Topics: Probabilita
Concepts: Combinazioni con ripetizione
Methods: Combinazioni ripetizione
Skills: Calcolo combinatorio
Exercise type: Problema combinatorio