Use the formula for nPr to solve the following question.
At a benefit concert, 10 bands have volunteered to perform but there is only enough time for 7 of the bands to play. How many lineups are possible?
We can use the formula for nPr to solve this question.
nPr = n! / (n-r)!
In this case, n = 10 (number of bands) and r = 7 (number of bands that can play).
So, using the formula:
10P7 = 10! / (10-7)!
= 10! / 3!
= (10*9*8*7*6*5*4*3*2*1) / (3*2*1)
= 3628800 / 6
= 604800
Therefore, there are 604800 possible lineups that can be formed with 7 out of 10 bands playing at the concert.