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.
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.