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
Answers
Answer:
5
Step-by-step explanation:
Given 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
Number of groups having 4 boys and one girl
= 4C4 x gC1 = g
Again number of groups having 3 boys and 2 girls
= 4C3 x gC1 = 2g(g - 1)
So number of dolls distributed will be
= g(1) + 2 x 2g(g - 1) = 4g^2 - 3g
According to question we have
4 g^2 - 3 g = 85
4 g^2 - 3 g - 85 = 0
4 g^2 - 20 g + 17 g - 85 = 0
4 g(g - 5) + 17(g - 5) = 0
(g - 5)(4 g + 17) = 0
g = 5 , - 17/4
So the value of g is 5
Answer:
5 is your answer.
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