Question

There are ten boys B₁, B₂, ...., B₁₀ and five girls G₁, G₂, ...., G₅ in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B₁ and B₂ together should not be the members of a group is ______.

Options

• 1120

• 1130

• 1140

• 1150

Answer 1

There are ten boys B₁, B₂, ...., B₁₀ and five girls G₁, G₂, ...., G₅ in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B₁ and B₂ together should not be the members of a group is 1120.

Explanation:

Let n(B) = 10

and n(g) = 5

The number of ways of forming a group of 3 girls of 3 boys.

= ⁵C₃ × ¹⁰C₃

= 80

Number of ways when boys B₁ of B₂ hot in the same group together

= 1200 × 80

= 1120