# Chapter 12 - Data Analysis and Probability - 12-6 Permutations and Combinations - Lesson Check - Page 765: 10

#### Work Step by Step

We can prove this easily with math. We know that n = r. We know that: $_nC_r =\frac{_nP_r}{r!} = \frac{n!}{(n-r)!r!}$ So it follows: $_nC_n =\frac{_nP_n}{n!} = \frac{n!}{(n-n)!n!}$ $\frac{n!}{0!n!}$ Since 0! = 1: $\frac{n!}{n!}$ = 1

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