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Question

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


A
15
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B
12
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C
8
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D
5
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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
$$=2\times 4\times ^{ g }{ { C }_{ 2 } }+g=4g^{ 2 }-3g=85$$
$$\Rightarrow g=5$$

Maths

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