A playschool contains 4 boys and y girls. On every Wednesday during winter, five students, of which at least three are boys, go to Zoological Garden, a different group being sent every week. At the Zoological Garden, each boy in the group is given a ball. If the total number of balls distributed is 368, then the value of y is
Explanation:
Since the group has to have atleast three boys, number of ways in which a group of five can be formed = (4C3 × yC2) + (4C4 × yC1) = [4 × (y)(y – 1)/2] + [(1)(y)] = 2y(y – 1) + y
Since each boy in the group gets a ball, total balls distributed = 3[2y(y – 1)] + 4y = 6y2 – 2y
Since total balls distributed= 368; 6y2 – 2y = 368
∴ 3y2 – y – 184 = 0
On solving this, y = 8
Hence, option (d).
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