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In how many different ways can the letters of the word “DETAIL” be arranged in such a way that the vowels occupy only the odd positions?1). 602). 363). 324). 28 |
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Answer» There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants Let the POSITIONS be marked as (1)(2)(3)(4)(5)(6) The 3 vowels can be placed at any of the 3 places marked (1)(3)(5) The number of ways of ARRANGING the vowels = 3P3 = 3! = 6 Also, the 3 consonants can be ARRANGED in the remaining 3 places The number of ways of these arrangements = 3P3 = 3! = 6 TOTAL number of ways = 6 × 6 = 36 ∴ Total number of ways = 36 |
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