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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?

1 Answer

6 votes

Answer:

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

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