Probability/Combinatorics Problem

These are due by Friday, so any help would be appreciated. Here is the problem:

A local company has two job openings available, and 160 people apply. Of the applicants, 50 are women.

**1. If two applicants are selected at random, what is the probability that both are men?**

And,

**2. If two persons are selected at random, what is the probability that exactly one is a woman?**

For the first one, I divided 110!/2!108! by 160!/2!158!, but the answer was wrong. I am almost certain the formula and math are correct. For the second problem, I am just completely lost, I don't know how to modify the formula to account for needing only one woman for the two applicants.

Thanks in advance.