A box contains 24 lightbulbs 2 of which are defective. If a person selects 10 lightbulbs at random without replacement, what is the probability that both defective bulbs will be selected?
I'm searching for the right way to select the sample space.
The denominator should be all the possible ways in which 10 balls can be selected from 24, i.e. ${24\choose 10}$
and the numerator should be all the possible ways in which the defective balls can be selected, but I can't decide whether that is: $2^{10}$ or just simply ${10\choose 2}$ can someone help clarify this?
EDIT:
second question:
Suppose that 35 people are divided in a random manner into two teams in such a way that one team contains 10 people and the other team contains 25 people. What is the probability that two particular people A and B will be on the same team?
i'm still having trouble finding the event space. The sample space should be all the possible ways in which 10 and 25 can be selected from 35, i.e. (35 choose 10)*(35 choose 10). But I have no idea how to find the event space... it seems like there are only 2 possibilities but I guess I'm wrong..