Question

If there are 60 books in the college library. In how many ways will these books be arranged on the shelves if 3 of the books are taken at a time with order of arrangement of the books considered

Answer 1

205,320

Explanation:

If order matters this is a permutation problem (as opposed to a combination problem). The permutation of this situation is

₆₀P₃ =
`(60!)/((60-3)!)` and is solved:

`(60*59*58*57!)/(57!)`

The 57 factorials cancel out, leaving us with 60*59*58 which comes to 205,320 different ways to pick 3 books if order matters.