Home > Permutations and Combinations > jee_main_2026_jan_21_shift_1 > df5ca40c43fc4631a807ca5ee941e75b
Not the exact question you were looking for?

Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.

Permutations and Combinations
Permutations with Repetition
jee_main_2026_jan_21_shift_1
Grade None

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 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 S such that only two digits are repeated and each of these is repeated exactly twice. Which of the following is true?
A. 45x = 7y
B. 29x = 5y
C. 56x = 9y
D. 21x = 4y

Step-by-Step Solution

Key Concept: Count permutations with specified repetition patterns.
Step 1: x = 9 × 8 × 9!/2! = 36 × 9!. Step 2: y = C(9,2) × C(7,5) × 9!/(2!2!) = 36 × 21 × 9!/4 = 189 × 9!. Step 3: x/y = 36/189 = 4/21. Step 4: Therefore 21x = 4y. This matches option D.
Correct Answer: D
Mathbee AI Mentor (Free Demo)

Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.

Master Permutations and Combinations with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free