Question

The word FACETIOUS is one of the only words in the English language to contain all five vowels in alphabetical order. If these nine letters are arranged randomly, what i:s the probability that the resulting "word" also contains the five vowels in order?

Answer 1

The word FACETIOUS is the only word in English which has all the vowels in alphabetical orders. The word has 9 letters which can be arranged in 9! Number of ways. A word is to be formed from there 9 letters such that the vowels are in alphabetical order. For the vowels to be in alphabetical order they should be arranged as AEIOU. There are 5! ways to arrange the 5 vowels and only one way will result in the required ordering of vowels in alphabetical order. So, the number of ways to arrange the letters such that the vowels are in alphabetical order 9! 51 =3024 So, the probability of arranging the letters such that the vowels are in alphabetical ordering 3024 =- 01=0.0083 Thus, the probability that a randomly selected word also contains vowels in alphabetical order is 0.0083.