JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(S=\{1,2,3,4,5,6,7,8,9\}\). Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let y be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,
- A \(29x=5y\)
- B \(45x=7y\)
- C \(21x=4y\)
- D \(56x=9y\)
Answer & Solution
Correct Answer
(C) \(21x=4y\)
Step-by-step Solution
Detailed explanation
\(S=\{1,2,3,.....,9\}\) \(x={}^{9}{C_{1}}.^{8}C_{7}\times\frac{9!}{2}=\frac{9\times8\times9!}{2}\) \(y={}^{9}{C_{2}}.^{7}C_{5}\times\frac{9!}{2!\times2!}=\frac{9\times8}{2}\times\frac{7\times6}{2}\times\frac{9!}{2!\times2!}\) \(\Rightarrow\frac{x}{y}=\frac{4}{21}\) \(21x=4y\)
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