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 :

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 : (A) 5 (B) 2 (C) 4 (D) 6

Tardigrade Admin · Accepted Answer

Total matches between boys of both team = 7 C 1 × 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 ⇒ n =4

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 :

5

2

4

6

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

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 :

5

2

4

6

Total matches between boys of both team =7C1​×4C1​=28 Total matches between girls of both team =nC1​6C1​=6n Now, 28+6n=52 ⇒n=4

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 :

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