How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
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!4! = 144
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!4! = 144