Question

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. \(21x=4y\)
• B. \(45x=7y\)
• C. \(56x=9y\)
• D. \(29x=5y\)

Hint:

In permutation problems with repetition, always divide by factorials of repeated elements to avoid overcounting.

Answer 1

The Correct Option is A