# The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is

Question:

The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is

(a) 574

(b) 36

(c) 754

(d) 144

Solution:

(d) 144

The word ARTICLE consists of 3 vowels that have to be arranged in the three even places. This can be done in 3! ways.

And, the remaining 4 consonants can be arranged among themselves in 4! ways.

∴ Total number of ways = 3!×">××4! = 144