A group of 9 workers decides to send a delegation of 3 to their supervisor to dicusss their grievences.

Question

c.) If there are 4 women and 5 men in the group, how many delegations would include at least 1 women?

I know I have to use combination C(9,1)x C(9,4) but I'm lost after that? Please help?

Answer 1

There are 9 of them so a delegation of 3 can go in 9C3 = 84 ways. There are 5 men in them so "all men" delgations will be 5C3= 10.
hence 84-10 = 74 delegations will contain at least one lady.
So what you have done and heard, both are wrong.

Answer 2

The number of possible delegations without considering any restriction is C(9,3) = 84.

The number of possible delegations which do not include any woman is C(5,3) = 10.

So the answer should be: 84-10 = 74.

I don't know how you get 129, and why is the answer 112. If you write your solution, I could check it to find the flaw (or maybe my solution is flawed).