Chapter 12.4, Problem 6CYU

To determine

To find: the permutation that the person can arrange the bins in a row.

Answer to Problem 6CYU

The person can arrange the bins in a row in 4 ways.

Explanation of Solution

Given information:

Total number of bins is 4.

Total recycling bin is 1.

Formula used:

  $P(n,r)=\frac{n!}{(n-r)!}$

Calculation :

Number of ways that the person can arrange the bins in a row -

  $\begin{array}{l}P(n,r)=\frac{n!}{(n-r)!}\\ P(4,1)=\frac{4!}{(4-1)!}\left[n=4\text{ and }r=1\right]\\ =\frac{4!}{3!}\left[\text{Simplify}\text{.}\right]\\ =\frac{4\times 3!}{3!}\left[\text{Divide by common factor}\text{.}\right]\\ =4\end{array}$

Hence, there are 4 ways that the person can arrange the bins in a row.