As to (a), the combinatorial argument:

What has C(2n, 2) to do with bowl of 2n marbles, numbered from 1 to 2n? Then imagine you divide the marbles over two bowls, each containing n marbles.

As to (b), the algebraic argument: write out the formulas...

PS. It is easier for quoting if you'd type out the exercise instead of attaching it as a JPG.