The number of ways in which the letters of the word ARTICLE
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) 4C3 × 4!

(c) 2 × 4!

(d) none of these.

Solution:

(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 4P3 ways.

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

$\therefore$ Total number of ways of arrangement $={ }^{4} P_{3} \times 4 !=4 ! \times 4 !=576$