Chapter 11.6, Problem 34E

To determine

To write: the expression for $20·19·18·17$ using factorial.

Answer to Problem 34E

The expression for $20·19·18·17$ using factorial is $P{}_4$ .

Explanation of Solution

Given :

  $20·19·18·17$ .

Formula used:

  $P{}_r=\frac{n!}{\left(n-r\right)!}$

Calculation : towrite the expression using factorial, first write $20!$ then divide it by $16!$ and according this data by using above formula write an expression.

  $\begin{array}{l}20·19·18·17=\frac{20!}{16!}\\ 20·19·18·17=\frac{20!}{\left(20-4\right)!}\\ 20·19·18·17=P{}_4\end{array}$

Hence,The expression for $20·19·18·17$ using factorial is $P{}_4$ .