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Question
How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
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Solution
The word ARTICLE consists of 3 vowels, which have to be arranged in 3 even places. This can be done in 3! ways.
Now, the remaining 4 consonants can be arranged in the remaining 4 places in 4! ways.
∴ Total number of words in which the vowels occupy only even places = 3!\[\times\]4! = 144
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