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 :

(1) 5

(2) 2

(3) 4

(4) 6

Answer 1

Correct answer is (3)

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