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 :
JEE · Math · previous-year question
- A.5
- B.2
- C.4correct
- D.6
Answer
C. 4
Explanation
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
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