A class contains 4 boys and g girls. Every sunday five students, including at least three boys go for a picnic to Zoo Park, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is

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Solution

The correct option is D 5
Different groups formed
$^{4} C_{3} \times^{g} C_{2} +^{4} C_{4} \times^{g} C_{1} = 4 \times^{g} C_{2} +^{g} C_{1}$

There are two girls in each of $4 \times^{g} C_{2}$ groups

No. of doll's distributed
$= 2 \times 4 \times^{g} C_{2} + g = 4 g^{2} - 3 g = 85$
$\Rightarrow g = 5$

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The correct option is D 5Different groups formed4C3×gC2+4C4×gC1=4×gC2+gC1There are two girls in each of 4×gC2groupsNo. of doll's distributed=2×4×gC2+g=4g2−3g=85⇒g=5