How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
Question:
How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
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
$\therefore$ Total number of words in which the vowels occupy only even places $=3 ! \times 4 !=144$