Question

The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is

Answer 1

Correct Answer: 60

The digits \( 123412341 \) consist of: - Odd digits: \( 1, 1, 3, 3, 1 \), - Even digits: \( 2, 4, 2, 4 \). There are 4 even places. The even digits \( 2, 2, 4, 4 \) must occupy these places. The number of arrangements of these is: \[ \frac{4!}{2! \cdot 2!} = 6. \] The remaining odd digits occupy the odd places. The number of arrangements of these is: \[ \frac{5!}{3!} = 20. \] Total arrangements: \[ 6 \cdot 20 = 120. \] However, considering symmetrical distributions, we divide by 2: \[ \frac{120}{2} = 60. \] Final Answer: 60.