Math Help - need help, on greatet integer function.

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

Rearranging, you get

Which equals

In plain English, you are picking objects from options and objects from options with regard to order. Thus, the term is simply dividing out all possible orderings of your objects.

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