A debate club consists of 6 girls and 4 boys. A team of 4 members is said to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is?

Given that there is at most one boy in the group of 4. Therefore the selection of 4 members team has 2 possibilities. They are

1. all 4 members are girls,
2. 3 girls and 1 boy
   From the first possibility we can select 4 members in 6C4 = 15 ways
   From the second possibility we can select 4 members in 6C3 × 4C1 = 20 × 4 = 80 ways
   Therefore we can select 4 members in 15 + 80 = 95 ways
   Captain can be selected from the group of 4 members in 4C1 = 4 ways
   Therefore, the number of ways of selecting a team of 4 members including the selection of captain is 95 × 4 = 380