combination

Question

Suppose 10 persons are in canteen whoch offers coffee,tea,pepsi How many ways they can order their drinks as a group  if each persin wants one of the 3 drinks ?

Answer 1

We have to divide 10 persons into 3 groups (corresponding to three drinks) such that a group may be empty. This is stars and bars problem Theorem 2(https://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29), and solution is given by $\binom{10+3-1}{3-1}=\binom{12}{2}=66$ ways.