Nine students reach the final of a quiz.

A permutation is an arrangement in a definite order. The number of ways to arrange $r$ of $n$ different objects is ${}^nP_r = n(n - 1)\cdots(n - r + 1) = \dfrac{n!}{(n - r)!}$, with $0! = 1$. If repeats are allowed, there are $n^r$ arrangements.