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 _____

We need to find the number of 9-digit numbers formed using all digits of 123412341, such that even digits occupy only even places.

The number 123412341 has 9 digits. Counting each digit:

- Digit 1 appears 3 times

- Digit 2 appears 2 times

- Digit 3 appears 2 times

- Digit 4 appears 2 times

Even digits: 2, 2, 4, 4 (4 even digits total)

Odd digits: 1, 1, 1, 3, 3 (5 odd digits total)

In a 9-digit number with positions numbered 1 through 9:

Even places: 2nd, 4th, 6th, 8th (4 even places)

Odd places: 1st, 3rd, 5th, 7th, 9th (5 odd places)

The condition states that even digits must occupy only even places. Since we have exactly 4 even digits and 4 even places, all even places must be filled with even digits, and all odd places must be filled with odd digits.

We need to arrange {2, 2, 4, 4} in 4 positions. The number of distinct arrangements of these 4 items (with repetitions) is:

We need to arrange {1, 1, 1, 3, 3} in 5 positions. The number of distinct arrangements is:

Since the arrangements in even places and odd places are independent, the total number of valid 9-digit numbers is:

The answer is 60.