Chapter 11.6, Problem 9E

To determine

To calculate: the number of permutations of four object taken three at a time.

Answer to Problem 9E

the number of permutations of four object taken three at a time is $4$ .

Explanation of Solution

Given :

Objects = $4$

Taken objects = $3$

Formula used:

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

Calculation : tofind thenumber of permutations of four objects taken three at a time, use the above formula and put the value in it.

  $\begin{array}{l}P{}_3=\frac{4!}{\left(4-3\right)!}\text{ [substitue n by 4 and r by 3]}\\ P{}_3=\frac{4·3·2·1}{1}\text{ [subtract, expand factorial, divide common factors] }\\ P{}_3=4\text{ [multiply]}\end{array}$

Hence,the number of permutations of four object taken three at a time is $4$ .