Four letter words will be made from the letters in the word BARNEY. No repetition of letters, and Y is not considered a vowel. What is the probability that two vowels will be side by side in the word?
I'm completely stuck on this question.
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Hint: There are two vowels
E. So 4-letter words with them side by side have one of the $6$ follows forms:
AE-- -AE- --AE EA-- -EA- --EA
Given any of these forms, how many ways can we add in the consonants? This gives the total number $N$ of 4-letter words with
E side by side. And the probability will be $N/^6 P_4=N/360$.