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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.