Final answer:
To find the number of committees with 3 boys and 2 girls that can be formed, we can use the concept of combinations. The total number of committees is calculated by multiplying the number of ways to choose 3 boys from a group of 10 by the number of ways to choose 2 girls from a group of 8. The final result is 3360 committees.
Step-by-step explanation:
To find the number of committees with 3 boys and 2 girls that can be formed from a class of 10 boys and 8 girls, we can use the concept of combinations. The number of ways to choose 3 boys from a group of 10 is given by the expression C(10, 3), which is calculated as 10! / (3!(10-3)!). Similarly, the number of ways to choose 2 girls from a group of 8 is given by C(8, 2). To find the total number of committees, we multiply these two values together, since the choices are independent: C(10, 3) * C(8, 2).
Substituting the values, we get C(10, 3) * C(8, 2) = (10! / (3!(10-3)!)) * (8! / (2!(8-2)!)) = (10*9*8 / (3*2*1)) * (8*7 / (2*1)) = 120 * 28 = 3360.
Therefore, there are 3360 committees of 3 boys and 2 girls that can be formed from the given class.