Combinations problem

[Zorber]

The number of combinations of 2 objects from n is equal to the number of combinations of 3 objects from n. Determine n.

The book says the answer is 5 but I can't get this. Any help please.

[KatieB]

n C 2 = n C 3

=> n! / [(n-2)!2!] = n!/ [(n-3)!3!]

=> (n-2)!2! = (n-3)!3!

=> 2(n-2) = 3!

=> 2n-4 = 6

=> 2n = 10

=> n = 5

[Zorber]

Cheers KatieB