Question

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

• A. $574$
• B. $36$
• C. $754$
• D. $144$

Answer 1

Answer: (D)

$144$

There are total $7$ words then there will be $7$ positions out of $3$ are even place like $2,4,6$ and we have $3$ vowels $A,I,E$

The vowels can be arranged in the even place in $3!$ places and the rest can be arranged in $4!$

$\therefore$ Required number of ways $3!\times 4!=144$