Need help with an advanced probablity/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.
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Here is # 1.

\(\displaystyle \frac{{\left( {\begin{array}{c} {110} \\ 2 \\ \end{array}} \right)}}{{\left( {\begin{array}{c} {160} \\ 2 \\\end{array}} \right)}}\)

Thanks for the swift response, however, I'm not entirely sure what to do with the answer though... Do I multiply each half of the formula and then divide or something else?

shaehl said:

Thanks for the swift response, however, I'm not entirely sure what to do with the answer though... Do I multiply each half of the formula and then divide or something else?

Click to expand...

I'm sorry, but I don't understand...? To which "halves" of what "formula" are you referring...?

Thank you!

Eliz.