The library is to be given 10 books as a gift. the books will be selected from a list of 22 titles. if each book selected must have a different title, how many possible selections are there

Answer: There are 646,646 different selections.

The library is going to select 10 books from a set of 22 books. There are a lot of different possibilities. This is a combination problem.

The standard notation is 22 C 10, this means that we are selecting 10 from 22 and the order doesn't matter. Most calculators will do this for you.

If you want to do the work by hand, evaluate: 22! / (10! x 12!)

Either way you will get 646,646 possibilities.