Question

At a benefit concert, fourteen bands have volunteered to perform but there is only enough time for six of the bands to play. How many lineups are possible?

Answer 1

3003

Explanation:

Total no. of bands volunteered to perform = 14

There is only enough time for 6 of the bands to play.

So, to find How many lineups are possible we will use combination:

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

n = 14

r = 6

So, no. of lineups are possible =
`^(14)C_6`

=
`(14!)/(6!(14-6)!)`

=
`(14!)/(6!(8)!)`

=
`(14* 13 * 12* 11* 10* 9)/(6 * 5* 4* 3* 2 * 1)`

=
`3003`

Hence 3003 lineups are possible .

Answer 2

we are given with a total of fourteen bands which we can choose from and choose six of them to play. we use comnbination instead of permutation because order of choosing in this case, is not important. The formula is 14C6 equal to 3003 ways