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?
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?
Answers
Answered by
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.
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.
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