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

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.

your formula becomes:

17! / ((4!*(17-4)!) which becomes:

17! / (4!*13!) as shown above.

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