use the formula for nPr to evaluate the following expression.

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

There are how many lineups.

3 answers

Since it is given that there are bands and only can perform, we can use the formula for permutations (nPr) to calculate the number of possible lineups.

nPr = n! / (n-r)!

In this case, n = total number of bands =
r = number of bands that will perform =

Plugging in the values:

nPr = ! / ( - )!
nPr = ! /

Using the formula for factorial:

nPr =! / ((-1)! * ((!-)!))
nPr = ! / !
nPr =

Therefore, there are possible lineups where bands will perform at the benefit concert.
give me a integer answer.
I apologize for the oversight. When calculating the permutations, we need to use the following formula:

nPr = n! / (n-r)!

Given that there are n = 7 bands and r = 5 bands will perform, we have:

7P5 = 7! / (7-5)!
7P5 = 7! / 2!
7P5 = 5040 / 2
7P5 = 2520

Therefore, there are 2520 possible lineups where 5 bands will perform at the concert.