Chapter 11 - Further Topics in Algebra - 11.6 Basics of Counting Theory - 11.6 Exercises - Page 1061: 19

$5$

$P(n,r)=\displaystyle \frac{n!}{(n-r)!}$. 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. --- $P(5,1)=\displaystyle \frac{5!}{(5-1)!}=\frac{5\times 4!}{4!}$ $=5$