### 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: To find the probability of an event, I need to divide the number of favorable outcomes by the total number of possible outcomes.
The total number of possible outcomes is the number of ways to choose 4 people from 20, which is 20 choose 4, or 20C4.
I can use the formula for combinations to calculate this: 20C4 = 20! / (4! * 16!) = 4845.
The number of favorable outcomes is the number of ways to choose 4 people with at least 1 boy and at least 1 girl.
This is the same as the number of ways to choose 4 people without choosing all boys or all girls.
The number of ways to choose 4 people with all boys is 10 choose 4, or 10C4.
Similarly, the number of ways to choose 4 people with all girls is 10C4.
I can use the same formula to calculate these: 10C4 = 10! / (4! * 6!) = 210.
Therefore, the number of ways to choose 4 people without choosing all boys or all girls is 20C4 - 10C4 - 10C4 = 4845 - 210 - 210 = 4425.
Now I can find the probability by dividing the favorable outcomes by the possible outcomes: 4425 / 4845 = 0.913.
This means that there is a 91.3% chance that the committee has at least 1 boy and at least 1 girl.