Question

A class has 4 boys and `g' girls. Every Sunday, 5 students including at least 3 boys go for a picnic to a doll house; a different group being sent every week. Every girl that goes on a trip gets a colour box. If 85 colour boxes were distributed after all possible groups went for picnic, then g =

• A. 7
• B. 6
• C. 5
• D. 4

Answer 1

The correct option is C 5

Number of groups with 3 boys ${=}^4{C}_3{\times }^g{C}_2=2g(g-1)$
Number of groups with 4 boys ${=}^4{C}_{\$}{\times }^g{C}_1=g$
Number of colour box distributed $=2g(g-1)\times 2+g\times 1=85\Rightarrow 4g^2-3g-85=0\Rightarrow (g-5)(4g+17)=0\Rightarrow g=5$