Chapter 8.5, Problem 26E

(a)

To determine

The total number different ways in which five girls and three boys walk through a doorway.

Answer to Problem 26E

40320 ways

Explanation of Solution

Given:

There are no restrictions.

Calculation:

Number of ways in which five girls and three boys can be arranged with no waking restrictions will be $\left(n_1+n_2\right)!$

  $\begin{array}{c}\left(5+3\right)!=8!\\ =40320\end{array}$

(b)

To determine

The total number different ways in which five girls and three boys walk through a doorway.

Answer to Problem 26E

720 ways

Explanation of Solution

Given:

The girls walk through before the boys.

Calculation:

Number of ways in which 5 girls can be walk through a doorway will be

  $\begin{array}{c}{m}_1=5!\\ =120\end{array}$

Number of ways in which 3 boys can be walk through a doorway will be

  $\begin{array}{c}{m}_2=3!\\ =6\end{array}$

According to Fundamental counting principle, the total number different ways in which five girls and three boys walk through a doorway will be

  $\begin{array}{c}{m}_1\times m_2=120\times 6\\ =720\end{array}$