Chapter 13, Problem 14RE

Choosing Seats If 4 people enter a bus that has 9 vacant seats, in how many ways can they be sealed?

To determine

To find: How many ways can four people be seated?

Answer to Problem 14RE

3024

Explanation of Solution

Given:

4 people enter a bus that has 9 vacant seats.

Formula used:

$P\left(n, r\right) = \frac{n!}{\left(n - r\right)!}$

Calculation:

4 people have to be seated in 9 vacant seat.

Here order is significant hence this is a case of permutation.

Number of ways 4 people can be seated is given by $P\left(9, 4\right)$.

$P\left(9, 4\right) = \frac{9!}{\left(9 - 4\right)!} = \frac{9!}{5!}$

$= 9*8*7*6*\frac{5!}{5!}$

$= 9*8*7*6$

$= 3024$

There are 3024 ways four people be seated in 9 vacant seats.