Question

You and three of your friends buy tickets for a concert so that you sit together in the same row. Write an expression using factorials that could be used to find the probability that you will get the seat on the far left.

Answer 1

`Pr = (1)/(4)`

Explanation:

Given

`n = 4`

Required

Probability that you seat on the far left

First, we calculate the total possible seat arrangements.

This is calculated using:

`Total =n!`

`Total =4!`

`Total =4*3*2*1`

`Total =24`

Next, the possible seat arrangements if you seat at the far left.

This implies that you can only seat 1 spot while your friends (3) can seat on any of the remaining 3 seats.

i.e.

`You \to 1`

`Friend\ 1,2,3 \to 3,2,1`

The number of arrangement is:

`Arrangement = 1 * 3 *2 *1`

`Arrangement = 6`

The required probability is:

`Pr = (Arrangement)/(Total)`

`Pr = (6)/(24)`

Simplify

`Pr = (1)/(4)`