combinatorial identities

Let n be a positive integer, then

(1)
(2)

Prove of (1):Let



Notice that:

So
we can select k(k<=n) a_is from Set A and select n-k b_is things from Set B
So we have ways

but it is equivalent to select n a_i s or b_i s from Set S because |S|=2n
So we obtain the rusult.

Prove of (2):

by the same property of Combinatorial number
we have:
 
So