Final answer:
To find the number of 5-person committees composed of three boys and two girls from four boys and four girls, we use combinations. By calculating each separately (4 choose 3 for boys and 4 choose 2 for girls) and multiplying them together, we find that there are 24 possible committees.
Step-by-step explanation:
To find the number of possible 5-person committees consisting of three boys and two girls that can be formed from a group of four boys and four girls, we use the concept of combinations, which is part of combinatorics in mathematics. We need to select three boys out of four and two girls out of four. The combinations for each group can be found using the combination formula, which is C(n, k) = n! / (k! * (n - k)!), where n is the total number of available choices, and k is the number of choices we want to make.
To calculate the number of ways to choose three boys out of four: C(4, 3) = 4! / (3! * (4 - 3)!) = 4.
Similarly, to calculate the number of ways to choose two girls out of four: C(4, 2) = 4! / (2! * (4 - 2)!) = 6.
The total number of committees is the product of the number of ways to choose the boys and the number of ways to choose the girls: 4 (for the boys) * 6 (for the girls) = 24 committees.