Hi! First time poster.
So I'm doing some homework, due in six hours. I'm almost done, but there's a couple of questions I'm not too sure of: one has to do with possibilities, the other not so much.
1. The easier one:
What is the coefficient of X^11 in (3 + X)^15?
I'm guessing it's 15!/11!4! = 1365 but that 3 in (X + 3)is making me uncomfortable.
The one that's bothering me:
2. Suppose that a class contains 12 men and 17 women.
(a) How many different 10 person teams can be made?
(b) How many different 5 person teams can be made that contain at least two men?
(a) Is it 19^10? That's the only thing I can think of (19 = 12 + 17) but for some reason I don't feel right about it.
(b) "At least". That "at least" changes everything. Any help would be appreciated.
Thanks in advance!