Find the number of ways of distributing 11 pastries of different flavors among 3 people such that everyone gets at least one pastry.

The this is the same as the number of onto functions from set A to set B where set A has 11 elements and set B has 3 elements.
The formula for onto functions is $$Sum(r = 1 to n) (-1)^r ^nC_r * r^m$$ where m is the number of elements in set A and n is the number of elements in set B.
Answer = $$3^{11} - 3 * 2^{11} + 3$$