How many permutations of [9] have no adjacent odd digits?
For example, a permutation like 385164927 is not allowed because 5 and 1 are adjacent.
Wouldn't the answer just be 4!5!? Since each even number must be placed between 2 odd numbers, we have 4! ways to arrange the even numbers. Then we have 5 spaces in between the odd numbers to arrange: so that would be 5!. Right?
Best Answer
As has already been stated in the comments, your approach and result are correct.