Question

A large van is being used for a picnic. There will be 8 people riding in the van, and there are 8 seats in the van (one of which is the driver's seat). One of the 8 people will have to drive, but only 4 of the people are licensed to drive the van. In how many different ways could the people seat themselves in the van so that they have a licensed driver

Answer 1

Answer:

The people can seat themselves in 20160 different ways.

Step-by-step explanation:

Arrangements of n elements:

The number of arrangements of n elements is given by the following formula:

$A_{n} = n!$

In this question:

For the first seat, that is, the driver seat, 4 possible people can sit.

For the remaining 7 seats, the number of ways in which the people can sit is an arrangement of 7 elements. So

$T = 4*7! = 4*5040 = 20160$

The people can seat themselves in 20160 different ways.