SOLUTION: There are entrees 17 available at a restaurant. From these, Archie is to choose 4 for his party. How many groups of 4 entrees can he choose, assuming that the order of the entree
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Question 239061: There are entrees 17 available at a restaurant. From these, Archie is to choose 4 for his party. How many groups of 4 entrees can he choose, assuming that the order of the entrees chosen does not matter? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! 17! / (4!*13!) = 17*16*15*14*13!/(4!*13!) = 17*16*15*14/(4*3*2) = 17*2*5*14 = 2380
smaller number lets you see it better.
assume 2 out of 5
5!/2!3! = 5*4/2 = 10
let abcde be the possible choice of entrees.
possible sets of 4 combinations (order not important) are:
ab
ac
ad
ae
bc
bd
be
cd
ce
de
your problem is the same with bigger numbers.
the formula for number of combinations is:
n! / (x!*(n-x)!)
where
n is the total number of possible entrees
x is the number of entrees in each set.
