# Team 'A' consists of 7 boys and n girls and

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 :

1. (1) 5

2. (2) 2

3. (3) 4

4. (4) 6

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, $28+6 n=52$

$\Rightarrow n=4$