How to solve "5Cn = 10"?

[clicknext]

This is in the notation for a combination, where the 5 and n are both subscripted.

For a simple one like this, it's easy enough to just guess, but is there a real way to solve it?

 

[Orsorum]

5!/(n!(5-n)!) = 10, right?

5!/10 = n!(5-n)! ==> 12 = n(n-1)(n-2)(n-3)...(5-n)(5-n-1)(5-n-2)...

Hmmm.

 

[clicknext]

Yes, my math teacher said he's never seen a way. =/

 

[Orsorum]

Actually, I don't think there's a solution to that problem, given that n < 5. There are at most 5 combinations.