SOLUTION: There are 18 entrees available at a restaurant. From these, Archie is to choose 4 for his party. How many groups of entrees can he choose, assuming that the order of the entrees c

Question 594161: There are 18 entrees available at a restaurant. From these, Archie is to choose 4 for his party. How many groups of entrees can he choose, assuming that the order of the entrees chosen does not matter?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
C(n,r) = (n!)/(r!(n-r)!)

C(18,4) = (18!)/(4!*(18-4)!)

C(18,4) = (18!)/(4!*14!)

C(18,4) = (18*17*16*15*14!)/(4!*14!)

C(18,4) = (18*17*16*15)/(4!)

C(18,4) = (18*17*16*15)/(4*3*2*1)

C(18,4) = (73440)/(24)

C(18,4) = 3060

So there are 3,060 different groups.
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