Question

A camp counselor and six campers are to be seated along a picnic bench. In how many ways could this be done if the counselor occupies the seat in the middle and the camper who tends to start food fights sits next to him (either on the left or on the right)

Answer 1

This can be done in 240 ways.

Explanation:

Number of arrangments:

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

`A_(n) = n!`

In this question:

7 people(camp counselor and six campers).

Camp counselor in the middle.

Camper who start food fights either to his left or to his right. For each of these cases, the other 5 campers are arranged in 5 positions. Then

How many ways:

`T = 2A_(5) = 2*(5!) = 240`

This can be done in 240 ways.