Question:
Team 'A' consists of 7 boys and $\mathrm{n}$ 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 $\mathrm{n}$ is equal to :
Correct Option: , 3
Solution:
Total matches between boys of both team
$={ }^{7} \mathrm{C}_{1} \times{ }^{4} \mathrm{C}_{1}=28$
Total matches between girls of both
team $={ }^{n} C_{1}{ }^{6} C_{1}=6 n$
Now, $28+6 n=52$
$\Rightarrow n=4$
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