The number of ways in which the letters of the word ARRANGE be arranged so that
(i) the two R's are never together,
(ii) the two A's are together but not two R's.
(iii) neither two A's nor two R's are together.

Answer

C

Explanation

The number of ways in which two A's are together
i.e., xAAxNxGxEx is `.^(5)C_(2)xx4!=240`
Hence, number of ways in which neigher two R's no two A's come together=900-240=660.