Question
In how many ways can the letters of the word
‘MEDICAL’ be rearranged so that the vowels never come together?Solution
Total number of letters in the word ‘MEDICAL’ = 7 The word MEDICAL consists of 7 letters in which E, I and A are three vowels. We get MDCL (EIA) keeping EIA together as single entity. Number of ways the letters can be formed when vowels are together = 5! × 3! = 720 Required number of arrangements when vowels are never together = 7! - 720 = 5040 – 720 = 4320
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