### 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: This is a probability problem involving combinations, so I need to count how many possible ways there are to form the committee, and how many of those ways satisfy the condition of having at least 1 boy and at least 1 girl.
To form a 5-person committee from 25 members, there are C(25,5) = 53130 possible ways, using the formula C(n,r) = n! / (r! * (n-r)!)
To have at least 1 boy and at least 1 girl, I need to avoid the cases where the committee is all boys or all girls.
There are C(10,5) = 252 ways to form an all-boys committee, and C(15,5) = 3003 ways to form an all-girls committee.
So the number of ways to form a committee with at least 1 boy and at least 1 girl is 53130 - 252 - 3003 = 49875