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 ___
Step-by-Step Solution
Key Concept: Even digits (2,4,2,4) occupy even places (4 places), odd digits (1,3,1,3,1) occupy odd places (5 places). Arrange each group accounting for repetitions.
Even places: 4 positions, digits 2,2,4,4 $\to$ 4!/(2!2!) = 6. Odd places: 5 positions, digits 1,1,1,3,3 $\to$ 5!/(3!2!) = 10. Total = 6 $\times$ 10 = 60.
Correct Answer: 60