Chapter 8.2, Problem 8.32E

(a)

To determine

To calculate how many different seating assignments are possible if there are $25$ seats in the classroom.

Answer to Problem 8.32E

  $1.55\times {10}^{25}$

Explanation of Solution

Use multiplication counting principle and that every time a person is seated one less person has to be seated:

  $\begin{array}{l}25\times 24\times \mathrm{....}\times 2\times 1\\ =25!\\ =1.55\times {10}^{25}\end{array}$

(b)

To determine

To calculate how many different seating assignments are possible if there are $30$ seats in the classroom.

Answer to Problem 8.32E

  $2.65\times {10}^{32}$

Explanation of Solution

Use multiplication counting principle and that every time a person is seated one less person has to be seated:

  $\begin{array}{l}30\times 29\times \mathrm{....}\times 2\times 1\\ =30!\\ =2.65\times {10}^{32}\end{array}$