It's no entirely clear whether you want a generating function for the answer or just need to use generating function techniques in deriving the answer. I'm going to assume the latter.

The first committee can be selected in ways, and then the subcommittee can be selected in ways; so the total number of ways the committee and subcommittee can be selected is

.

Let's start by finding f(x), the ordinary power series generating function for the number of ways to select the committee. From the binomial theorem,

.... (1), and

.... (2)

Subtracting (2) from (1) and dividing by 2, we have

.... (3)

Let ; then

Using the same trick to isolate the even powers of y that we used to find f, but this time adding instead of subtracting, we have

.

Let y = 1; then

.

Substituting from (3),

,

i.e, the total number of ways to select the committee and subcommittee is

.