### Instruction: The Grammar club has 20 members: 10 boys and 10 girls.  A 4-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 total number of ways to choose a 4-person committee from 20 people, and the number of ways to choose a committee that has only boys or only girls.
The total number of ways to choose 4 people out of 20 is given by the binomial coefficient (20 choose 4), which is 20!/(4!)(16!) = 4845.
The number of ways to choose a committee of 4 boys out of 10 boys is (10 choose 4), which is 10!/(4!)(6!) = 210.
The number of ways to choose a committee of 4 girls out of 10 girls is also (10 choose 4) = 210.
So the number of ways to choose a committee that has only boys or only girls is 210 + 210 = 420.
Therefore, the number of ways to choose a committee that has at least 1 boy and at least 1 girl is 4845 - 420 = 4425.
The probability of choosing such a committee is the ratio of the favorable outcomes to the total outcomes, which is 4425/4845 = 0.913.