The word FACETIOUS is the most common word in the English language which has each of the five vowels in order from left to right. How many ways can the letters in the word FACETIOUS be arranged such that all five vowels are in order from left to right?
I am wondering if there is an easier way than bashing and counting all the possiblities.
Best Answer
We start with $9!$ and divide by $5!$ to account for the vowels. This is because there are $9!$ permutations without the extra restriction, and then one in every $5!$ of them have the vowels in the desired order. The answer is $3024.$