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Solution Find all the possible scenarios where vowels come together and subtract it from the total words possibleThe word LETTER has 6 alphabets of which 2 are repeated twice.The total number of 6 letter words =6!2!2!=6×5×4×3×22×2=180 wordsThere are 2 vowels in the word LETTER, that is, (EE).If EE are assumed to be together they can be arranged in 5!2! ways.So, the words where vowels are together are 5!2!=1202=60 Thus, the total number of words where vowels are not together=180-60=120Hence, there are 120 words formed from the word LETTER where no vowels are together.In how many different ways can the letters of the word EXTRA be arranged so that the vowels are never together?A. 120 B. 48 C. 72 D. 168 E. None of these Answer: Option C Solution(By Examveda Team) Taking the vowels (EA) as one letter, the given word has the letters XTR (EA), i.e., 4 letters. Click here to read 1000+ Related Questions on Permutation and Combination(Arithmetic Ability)Disclaimer The questions posted on the site are solely user generated, Doubtnut has no ownership or control over the nature and content of those questions. Doubtnut is not responsible for any discrepancies concerning the duplicity of content over those questions. How many words can be formed from the letters of the word extra so the vowels are always together?= 2 ways. Number of words each having vowels together = 24 x 2 = 48 ways. Total number of words formed by using all the letters of the given words = 5!
How many words are there in which vowels are never together?number of arrangements in which the vowels do not come together =5040−1440=3600 ways.
Is there a 5 letter word with all vowels?Unfortunately, there are no words in English that are made up entirely of vowels, so we will have to settle for the next best thing: a five-letter word containing four of them.
What 6 letter word has all vowels?Eunoia, at six letters long, is the shortest word in the English language that contains all five main vowels.
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