So, most combinatorics I've looked at while researching this consist of limiting the number of selections made from a set X and working out the probability of a particular combination of results.
In this instance I actually want to work out the average number of times I have to select an item from the set X, assuming replacement, before I have selected each item at least once. Now I can do this via an iterative process whereby I just run a selection loop until such time as I get each item at least once and then average several thousand iterations.
However, I am curious if it's possible to calculate this average in a more formulaic method.