Team A consists of 7 boys and n girls, and Team B has 4 boys and 6 girls.

Question

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:

Accepted Answer

Total matches between boys of both team = $${}^7{C_1} \times {}^4{C_1} = 28$$

Total matches between girls of both team = $${}^n{C_1}\,{}^6{C_1} = 6n$$

Now, 28 + 6n = 52

$$ \Rightarrow $$ n = 4

Solutions · 1