In how many ways can a group of 5 members be formed by selecting 3 boys out of…

Step-by-Step Solution

1. Select the boys: We need to choose 3 boys out of 6. This is a combination problem where order does not matter. The formula for combinations is C(n, r) = n! / [r! * (n - r)!].

   • C(6, 3) = 6! / [3! * (6 - 3)!]

   • C(6, 3) = (6 * 5 * 4) / (3 * 2 * 1)

   • C(6, 3) = 20 ways.

2. Select the girls: We need to choose 2 girls out of 5.

   • C(5, 2) = 5! / [2! * (5 - 2)!]

   • C(5, 2) = (5 * 4) / (2 * 1)

   • C(5, 2) = 10 ways.

3. Calculate the total ways: Since we need to select both boys AND girls to form the group, we multiply the number of ways to select the boys by the number of ways to select the girls.

   • Total ways = 20 * 10 = 200 ways.