SOLUTION: An entertainment hall must select 6 of 18 possible entertainers for its summer schedule. In how many ways can that be done?

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Question 970886: An entertainment hall must select 6 of 18 possible entertainers for its summer schedule. In how many ways can that be done?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
It is asking to compute C(18,6)

C(n,r) = (n!)/(r!(n-r)!)

C(18,6) = (18!)/(6!*(18-6)!)

C(18,6) = (18!)/(6!*12!)

C(18,6) = (18*17*16*15*14*13*12!)/(6!*12!)

C(18,6) = (18*17*16*15*14*13)/(6!)

C(18,6) = (18*17*16*15*14*13)/(6*5*4*3*2*1)

C(18,6) = (13366080)/(720)

C(18,6) = 18564

So there are 18564 ways to pick 6 people from a pool of 18. Order does not matter.