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
4C3 × 4!
2 × 4!
none of these.
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 x 4! = 4! x 4! = 576
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