### Instruction: The science club has 25 members: 10 boys and 15 girls.  A 5-person committee is chosen at random.  What is the probability that the committee has at least 1 boy and at least 1 girl?### Response: I need to find the fraction of all possible committees that have at least 1 boy and at least 1 girl.
One way to do this is to subtract the fraction of committees that have only boys or only girls from 1.
The total number of ways to choose 5 people from 25 is 25 choose 5, which is 53130.
The number of ways to choose 5 boys from 10 boys is 10 choose 5, which is 252.
The number of ways to choose 5 girls from 15 girls is 15 choose 5, which is 3003.
So the number of ways to choose only boys or only girls is 252 + 3003, which is 3255.
Therefore, the fraction of committees that have only boys or only girls is 3255/53130, which is about 0.0613.
Subtracting this from 1, I get the fraction of committees that have at least 1 boy and at least 1 girl, which is 1 - 0.0613, which is about 0.9387.