### Home > A2C > Chapter 12 > Lesson 12.4.2 > Problem12-189

12-189.

You know that $_ { n } C _ { r } = \frac { n ! } { ( n - r ) ! r ! }$ and$_ { n } C _ { r } = \frac { n P _ { r } } { r ! }$. Show that the formulas are equivalent.

${\text{Recall that }_{n}P_{r}=\frac{n!}{(n-r)!}.}$

$\text{Use the Associative Property to make }_nC_r = \frac{n!}{(n-r)!}\cdot \frac{1}{r!}$