Question

At a benefit concert, nine bands have volunteered to perform but there is only enough time for seven of the bands to play. How many lineups are lineups (Simplify your answer. Type an integer or a fraction.)

Answer 1

Answer: Hi, so here you have 9 bands and time fo only 7, then if the order matters, for the first band you have 9 options, for the second you have 8 options (because one of them already played), for the third band you have 7 options, and so on.

the total number of combinations is 9*8*7*6*5*4*3 = 181440 combinations

If the order of the band doesn't matter, then you need to do the combinatory between 9 and 7 is:

$\frac{9!}{(9-7)!*7!} = 9*8/(*2)$ = 36 combinations, that is the same of dividing 181440 by 7!.