(a) is just evaluating each:

(b)

The second method is doing what i did for question two in your previous post, but at the end change C(5,1) to C(5,4) and C(6,2) to C(6,4), why can we do that?

C(n,r) = C(n, n - r)

so, for example, C(6,2) = C(6, 6 - 2) = C(6,4)