What is the shortest solution to the following problem?
What is the number of ways to order the 26 letters of alphabet so that no two of the vowels a,e,i,o,u occur consecutively?
What I thought is to subtract permutations consisting of 2 vowels, 3 vowels, 4 vowels and 5 vowels occurring consecutively from all permutations 26!. But I could not even find an reasonable answer with that method. It seems to be too long and I always make mistakes.