Chapter 13.1, Problem 17E

To determine

To calculate: The number of different ways to schedule 7 classes.

Answer to Problem 17E

The number of different ways to schedule 7 classesare $5040$ .

Explanation of Solution

Given information:

The 7 classes are to be scheduled and each class is offered in each of 7 periods.

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 provided information that 7 classes are to be scheduled and each class is offered in each of 7 periods.

To schedule 7 classes, there are 7 choices to select from in first period then6 ways to select from for second period, 5 ways select from for third period

Therefore, number of ways are $P\left(7,7\right)$

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 7.

  $\begin{array}{c}P\left(7,7\right)=7!\\ =7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1\\ =5040\end{array}$

Thus, the number of different ways to schedule 7 classes are $5040$ .