This method of counting the same thing two ways to show that an equation holds is quite frequently used in combinatorics. It's called the "counting two ways" method of proof (you guessed it, I suppose).
Now try to guess what the left side of the second equation may be counting. From the right side you get the hint that it is probably also a somewhat complicated way of counting all the subsets of size r of a set of size n.
They are not showing because you need to wrap them in math ... /math tags.* I dont know why my latex symbols are not showing...*