Number of ways to get a 10-person committee
How many ways are there to form a 10-person committee from 13 women and 18 men so that there is at least one woman on the committee?
Okay, I think I know what to do with this, but I want to be sure I going about it the right way. I will use (n)C(k) as notation for "n choose k".
First, the number of total committees regardless of gender would be (31)C(10). Then I just subtract the number of ways to get a committee of all men, which would be (18)C(10). So my final answer would be (31)C(10) - (18)C(10). Is this correct?