# Chapter 13 - Probability - 13-3 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 841: 13

$10,897,286,400$

#### Work Step by Step

We start with the given expression: $\frac{15!}{(15-10)!}$ First, we simplify inside of the parentheses in the denominator: $\frac{15!}{5!}$ To evaluate a factorial expression, we multiply the number by each of the preceding integers until we get to $1$. So, $\frac{15!}{5!}=\frac{15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{5\times4\times3\times2\times1}=15\times14\times13\times12\times11\times10\times9\times8\times7\times6=10,897,286,400$

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