Math Help - need help, on greatet integer function.

1. need help, on greatet integer function.

Show that (2a)!(2b)!/(a!b!(a + b)!) is an integer.

2. A "verbal" proof?

Rearranging, you get $\frac{(2a)!}{a!}*\frac{(2b)!}{b!}*\frac{1}{(a+b)!}$

Which equals $\frac{(_{2a}P_a)*(_{2b}P_b)}{(a+b)!}$

In plain English, you are picking $a$ objects from $2a$ options and $b$ objects from $2b$ options with regard to order. Thus, the $(a+b)!$ term is simply dividing out all possible orderings of your $a+b$ objects.

I am sure someone can come up with a formal proof, but this at least should be convincing