Question

Noam chose 3 songs from a pile of 20 songs to play at a piano recital. What is the probability that she chose The

Entertainer, Something Doing, and The Ragtime Dance?

Answer 1

`Pr=(1)/(1,140)`

Explanation:

The probability definition is

`Pr=\frac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}`

1. The number of favorable outcomes is 1, because there is the only way to choose The Entertainer, Something Doing, and The Ragtime Dance.

2. The number of all possible outcomes is

`C^(20)_3=(20!)/(3!(20-3)!)=(17!\cdot 18\cdot 19\cdot 20)/(2\cdot 3\cdot 17!)=(18\cdot 19\cdot 20)/(6)=3\cdot 19\cdot 20=1,140`

Hence, the probability is

`Pr=(1)/(1,140)`