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Maths-

General

Easy

Question

A class contains 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, 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 -

15
12
8
5

The correct answer is: 5

Number of groups having 4 boys and 1 girl
= (⁴C₄) (^gC₁) = g
and number of groups having 3 boys and 2 girls
= (⁴C₃) (^gC₂) = 2g(g – 1)
Thus, the number of dolls distributed
= g(1) + (2)[2g (g – 1)]
= 4g² – 3g
We are given 4g² – 3g = 85 $rightwards double arrow$ g = 5.

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