Suppose there are 5 types of toys, which you are collecting one by one, with the goal of getting a complete set. When collecting toys, the toy types are random (as is sometimes the case, for example, with toys included in cereal boxes or included with kids meals from a fast food restaurant). Assume that each time you collect a toy, it is equally likely to be any of the 5 types. What is the expected number of toys needed until you have a complete set?

Hints:

(1) First, find the expected number of toys until you have some type, then the expected number of toys until you have a new type (after that you already have a type), and so on.

(2) Related to Geometric model.