Permutations.

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 be included at most one boy, then the number of ways of selecting the team is

Expert Solution

Given that there is atmost one boy in the group of 4.

Therefore the selection of 4 members team has 2 possibilities.

a) all 4 members are girls

b) 3 girls and 1 boy

From the first possibility, we can select 4 members in ⁶C4 ways = 15 ways

From the second possibility, we can select 4 members in ⁶C3. 4C1 = 80 ways

Total number of ways = 15+80 = 95

So we can select 4 members in 95 ways.

The captain can be selected from the group of 4 members in ⁴C1 = 4 ways

So the number of ways of selecting the team of 4 members including the selection of captain is

95× 4 = 380

Number of ways of selecting the team of 4 members including the selection of captain is 380.

Nikhil Thakur answered 3 years ago

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