Chapter 4, Problem 3E

To determine

To calculate: The number of different arrangement of 8 sweaters.

Answer to Problem 3E

The number of different arrangement of 8 sweatersare $280$ .

Explanation of Solution

Given information:

4 identical red sweaters, 3 identical brown sweaters and 1 white sweater are in the store.

Formula used:

If there are n objects taken n at a time then permutation is defined as $P\left(n,n\right)=n!$ .

Calculation:

Consider the information that 4 identical red sweaters, 3 identical brown sweaters and 1 white sweater are in the store.

To arrange 8 sweaters in a row.

Recall that if there are n objects taken n at a time then permutation is defined as $P\left(n,n\right)=n!$ .

Here n is 8 but a few of them are identical.

  $\begin{array}{c}\frac{8!}{4!3!1!}=\frac{8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{\left(4\cdot 3\cdot 2\cdot 1\right)\left(3\cdot 2\cdot 1\right)}\\ =280\end{array}$

Thus, the number of different arrangement of 8 sweaters are $280$ .