# Chapter 12 - Counting and Probability - Section 12.2 Permutations and Combinations - 12.2 Assess Your Understanding - Page 875: 41

$35$

#### Work Step by Step

This involves combination (because order does not matter) in which $n=7$ and $r=4$. Using the formula $C(n,r)=\dfrac{n!}{(n-r)!\times r!}$ gives: $C(7,4) \\=\dfrac{7!}{(7-4)!4!} \\= \dfrac{7!}{3!\times4!} \\= \dfrac{7\times6\times5\times4!}{3!\times4!} \\= \dfrac{7\times6\times5}{3!} \\=\dfrac{210}{6} \\= 35$

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