$$Total\ potential\ gifts\ =10\ gifts$$
$$Carol\ cano\ nly\ afford\ to\ buy=2\ gifts$$
$$So,\ \ Carol\ will\ be\ selecting\ 2\ out\ of\ 10\ gifts=>$$
$$10C2\ which\ is\ in\ forn\ nCr$$
$$=>\ \frac{n!}{r!\cdot\left(n-r\right)!}$$
$$=>\frac{10!}{2!\cdot\left(10-2\right)!}$$
$$=>\frac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{2\cdot1\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}$$
$$=>\frac{10\cdot9}{2\cdot1}$$
$$=>\frac{90}{2}$$
$$=>45$$
$$Answer\ =\ C$$