Chapter 12.6, Problem 3P

Six runners are available for the 400-meter relay. Four runners are needed to run 100 m a piece, in a specified order. How many different runner lineups can the coach consider for the relay with one of each?

To determine

Find the number of different runner lineups that the coach can consider for the relay with one of each.

Answer to Problem 3P

360

Explanation of Solution

Given:

Six runners are available for the 400-meter relay.Four runners are needed to run 100m a piece, in a specified order.

Calculation:

The number of different runner lineups that the coach can consider for the relay with one of each can be found out by permutation .

We need to choose 4 out of 6 runners and since the lineups are different , so the number will be = $P{}_4=\frac{6!}{(6-4)!}=\frac{6!}{2!}=6\cdot 5\cdot 4\cdot 3=360$ .