A class consists of $$4$$ 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

Question

Infinity Learn · Accepted Answer

Number of groups having $$4$$ boys and $$1$$ girl $$=$$ $$4C4$$ $$8C1=gand$$ number of groups having $$3$$ boys and $$2$$ $$girls=$$ $$4C3$$ $$gC2=2g(g$$−$$1)Thus$$, the number of dolls $$distributed=g(1)+(2)$$[$$2g(g$$−$$1)$$]$$=4g2$$−$$3gWe$$ are given $$4g2$$−$$3g=85$$⇒$$g=5$$

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