Question

There are 18 finalists in a singing competition. The top six singers receive prizes. How many ways can the singers finish first through sixth​?

Answer 1

In this case, the order matters, so this is a permutation problem.
You need to pick 6 out of 18.


`_(n)P_(r) = (n!)/((n - r)!)`


`_(18)P_(6) = (18!)/((18 - 6)!)`


`_(18)P_(6) = (18!)/(12!)`


`_(18)P_(6) = (18 * 17 * 16 * 15 * 14 * 13 * 12!)/(12!)`


`_(18)P_(6) = 18 * 17 * 16 * 15 * 14 * 13`


`_(18)P_(6) = 13,366,080`