JEE Mains · Maths · STD 11 - 6. permutation and combination
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 \(6\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
Total matches between boys of both team \(={ }^{7} C _{1} \times{ }^{4} C _{1}=28\) Total matches between girls of both team \(={ }^{n} C_{1}{ }^{6} C_{1}=6 n\) Now, \(28+6 n=52\) \(\Rightarrow n =4\)
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