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  4. Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :

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Q. Team 'A' consists of $7$ boys and $n$ girls and Team 'B' has 4 boys and $6$ girls. If a total of $52$ single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then $n$ is equal to :

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Solution:

Total matches between boys of both team
$={ }^{7} C _{1} \times{ }^{4} C _{1}=28$
Total matches between girls of both
$\text { team }={ }^{ n } C _{1}{ }^{6} C _{1}=6 n$
Now, $28+6 n=52$
$\Rightarrow n =4$