Chapter 11 - Further Topics in Algebra - 11.6 Basics of Counting Theory - 11.6 Exercises - Page 1061: 22

$84$

$C(n,r)=\displaystyle \frac{n!}{(n-r)!r!}$. Factorials: $n!=n(n-1)!=n(n-1)(n-2)!=...$ $n!=n(n-1)(n-2)\cdots(3)(2)(1)$ $ 0!=1,\qquad$ by definition. --- $C(9,3)=\displaystyle \frac{9!}{(9-3)!3!}=\frac{9\times 8\times 7\times(6!)}{(6!)3!}$ $=\displaystyle \frac{9\times 8\times 7}{3\times 2\times 1}$ $=3\times 4\times 7$ = $84$