Question 239061
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.