Finding the Number of Permutations Using the Formula

A professor is creating an exam of 9 questions from a test bank of 12 questions. How many ways can she select and arrange the questions?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Substitute $n = 12$ and $r = 9$ into the permutation formula and simplify.

$\begin{array}{l} P (n, r) = \frac{n!}{(n - r)!} \\ P (12, 9) = \frac{12!}{(12 - 9)!} = \frac{12!}{3!} = 79, 833, 600 \end{array}$
There are 79,833,600 possible permutations of exam questions!

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

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