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
B
12
C
8
D
5

Solution

## The correct option is D 5Different 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 $$4\times ^{ g }{ { C }_{ 2 } }$$groupsNo. of doll's distributed$$=2\times 4\times ^{ g }{ { C }_{ 2 } }+g=4g^{ 2 }-3g=85$$$$\Rightarrow g=5$$Maths

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