Question 427273
the general formula is:


c(n,r) = n! / (r! * (n-r)!)


the numerator will always be the same.


the denominator also has to be the same.


in order for this to happen, then r! and (n-r)! have to be reversed.


example:


1! * 17! = 17! * 1!


on the left side of the equation, r = 1 and n-r = 17
on the right sides of the equation, r = 17 and n-r = 1


you will get 1! * 17! = 17! * 1! yielding the same denominator.


the difference between the 2, however, is not equal to 2.


when r and n-r get closer together, the difference will be 2.


if we pick 8 as r, then n-r becomes 10.


reversing them, we get r = 10 and n-r = 8.


this satisfies the condition we are looking for so the answer will be r = 8.


with r = 8, the formula becomes c(18,8)
with r = 10, the formula becomes c(18,10)


c(18,8) = 18! / (8! * 10!)
c(18,10) = 18! / (10! * 8!)


the numerator is always the same.
the denominator is the same as well, only commuted.


a*b = b*a is the basic commutative property which is why i say the denominator is commuted.


that's your answer.


r = 8.