Probability problem: random selection of shoes

I'm sure a lot of people have seen questions like this one. I've gotten half of it done, but I could use a hand with the other half.

A large box contains 10 pairs of shoes. If 6 shoes are selected at random, what is the probability of:

a) no complete pairs

My answer: $\displaystyle P=\frac{\left(\begin{array}{cc}10\\6\end{array}\ri ght) 2^6}{\left(\begin{array}{cc}20\\6\end{array}\right )}$

b) exactly one complete pair

My answer: $\displaystyle P=\frac{10 \left(\begin{array}{cc}9\\4\end{array}\right) 2^4}{\left(\begin{array}{cc}20\\6\end{array}\right )}$

c) exactly two complete pairs

d) exactly three complete pairs

I could use a hand with the latter two.