Question

The number of ways in which the letters of the word Article can be arranged so that even places are always occupied by consonants is

• A. 576
• B. ${}^4{C}_3\times 4!$
• C. $2\times 4!$
• D. None of these

Answer 1

The correct option is A

576

There are 3 even places in the 7 letter word ARTICLE.

So, we have to arrange 4 consonants in these 3 places in ${}^4{P}_3$ ways.

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

$\therefore$ Total number of ways of arrangement =
${}^4{P}_3\times 4!=4!\times 4!=576$