Answer:
There are 495 different lineups
Step-by-step explanation:
If we have a set of N elements, the total number of different combinations of K elements (such that K ≤ N) is given by:
[tex]C (N, K) = \frac{N!}{(N - K)!*K!}[/tex]
In this case, we have 12 bands, but we can only select 8 of them.
Then we have N = 12, and K = 8.
Using the above formula, we can conclude that the total number of possible lineups (combinations of bands) is:
[tex]C (12, 8) = \frac{12!}{(12 - 8)!*8!} = \frac{12!}{(4)!*8!} = \frac{12*11*10*9}{4*3*2} = 495[/tex]
There are 495 different lineups
