The number of ways in which the letters of the word ARRANGE be arranged so that “neither two A’s nor two R’s are together”

There are in all 900 which in each of which tow R’s are never together. Consider any such word. Either the two A’s are together or the two A’s are not together But the no. of all such arrangements in which the two A’s are together is 240.

The no. of arrangements in which two A’s are not together is  $900-240=660$