There are 7 friends A, B, C, D, E, F, and G that belong to a classroom of 35 students. Three students are chosen from the 35.
What the probability that exactly two of the group of friends is chosen?
Probability that exactly none of the seven friends are chosen?
. . . . .
So I know the total number of combinations of 3 students chosen out of 35 is (35 c 3). That is the denominator for these questions. I can't figure out what the numerator should be.
Is it (7 c 2)/(35 c 3) and (7 c 0)/(35 c 3) ? This does not seem correct.
The number (7 c 2) I chose because I need 2 member from this group of seven, and there are (7 c 2) combinations of getting (AB, BC, AD, FE, etc). On second thought, I might also want to include the possibility ways of getting a single non-friend member for the last slot, so it the numerator:
(7 c 2)*(35 - 7) ?
Then for no friends, it would be (7 c 0)*(35)(34)(33) as the numerator. Because there are three slots for non-friends?