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.

Answer 1

(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.
∴ Total number of ways of arrangement = ⁴P₃ $\times$4! = 4!$\times$4! = 576