Question

Use the formula for Subscript n Baseline Upper P Subscript r to solve the following question.

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we can use the formula for permutations of choosing r items from a set of n items:

Subscript n Baseline Upper P Subscript r = n! / (n-r)!

In this case, we have 14 bands and we want to choose 7 of them to perform. Using the formula, we have:

Subscript 14 Baseline Upper P Subscript 7 = 14! / (14-7)!
= 14! / 7!
= (14 x 13 x 12 x 11 x 10 x 9 x 8) / (7 x 6 x 5 x 4 x 3 x 2 x 1)
= 32,186,400 / 5,040
= 6,384

Therefore, there are 6,384 possible lineups for the benefit concert.