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

Answer:

The total number of possible outcomes = 455

Step-by-step 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:

$_nC_r=\frac{n!}{r!(n-r)!}$

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

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

Plugging in the known values:

$15C3$

⇒ $\frac{15!}{3!(15-3)!}$

⇒  $\frac{15!}{3!(12)!}$

⇒ $\frac{15\times14\times13\times12!}{3!\times12!}$ [Canceling out the common terms]

⇒ $\frac{15\times14\times13}{3\times2\times1}$

⇒ $455$