Question

You are the 100th customer to enter a video store, and you are entitled to a prize of 3 video games. You have 15 games to choose from, and they must be chosen at random.

What is the total number of possible outcomes?

Answer 1

The total number of possible outcomes = 455

Explanation:

Given:

Total number of games = 15

Number of games to be chosen = 3

The total number of ways in which the 3 games out of 15 be choosen can be given by:

`_nC_r=(n!)/(r!(n-r)!)`

where
`n\rightarrow` represents total number of games and

`r\rightarrow` represents the number of choices to be made.

Plugging in the known values:

`15C3`

⇒
`(15!)/(3!(15-3)!)`

⇒
`(15!)/(3!(12)!)`

⇒
`(15*14*13*12!)/(3!*12!)` [Canceling out the common terms]

⇒
`(15*14*13)/(3*2*1)`

⇒
`455`