Question

At a benefit concert, nine bands have volunteered to perform but there is only enough time for five of the bands to

play. How many lineups are possible?

Answer 1

126 lineups

Explanation:

This is a problem in combinatorics which asks in how many ways can a subset of 5 be formed from a larger set of 9

In general, if you were to see how many ways a subset of
`r` can be formed from a larger subset
`n` denoted by
`nC_r` we use the formula

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

There are calculators that can compute this and I used a scientific calculator to do so.

`9C_5 = 126`