Chapter 11, Problem 17CT

To determine

To calculate: the ways of display four different types of sweaters.

Answer to Problem 17CT

Yes, we counted it using permutations. The ways of display four different types of sweaters is $11880$ .

Explanation of Solution

Given information :

total sweaters = $12$

display sweaters = $4$

Formula used:

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

Calculation : to find the ways display four different types of sweaters is , use the permutation.

Now, take four sweaters from 12 sweaters,

  $\begin{array}{l}P{}_r=\frac{n!}{\left(n-r\right)!}\\ P{}_4=\frac{12!}{\left(12-4\right)!}\text{ [substitue n by 12 and r by 4]}\\ P{}_4=\frac{12!}{8!}\text{ [subtract]}\\ P{}_4=11880\text{ [divide out common factors and multiply]}\end{array}$

Hence,Yes, we counted it using permutations. The ways of display four different types of sweaters is $11880$ .