How many ways can 9 people line up for a photographer if..

Question

How many ways can 9 people line up for a photographer if

a) there are no restrictions?

b) Johnny needs to be in the middle?

c) Amy and Peter need to be at the ends, and Johnny is in the middle?

Answer 1

I believe you would go about solving the problems like this:

For question a, the answer would be 9!

9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880

There are 362,880 ways 9 people can line up with no restrictions.

For question b, the answer would be 40,320. There's only 1 way Johnny can be in the middle so you do: 9 - 1 = 8

8! = 40,320.

For question c, the answer would be 1,440:

6! * 2! = 1,440.

The 6! is the total number of people minus the three people that are in a specific area in the line (9 - 3). The 2! is the number of ways Amy and Peter can be at both ends (Amy on the left, Peter on the right. OR, Peter on the left, Amy on the right).