Question

A coordinator will select 6 songs from a list of 9 songs to compose an event's musical entertainment lineup. How many different lineups are possible?

Answer 1

Answer:

84 different lineups are possible

Step-by-step explanation:

The order in which the songs are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

6 musics from a set of 9. So

$C_{9,6} = \frac{9!}{6!(9-6)!} = 84$

84 different lineups are possible