The word ARRANGE consists of 7 letters with 2 A's, 2 R's, and 3 other distinct consonants (N, G, E), giving a total of 7!/(2!2!) = 1260 arrangements. To find the arrangements where no two A's are together, we first arrange the remaining 5 letters (2 R's, N, G, E), which can be done in 5!/2! = 60 ways. This arrangement creates 6 gaps (including the ends) where the 2 identical A's can be placed to ensure they are separated. Selecting 2 out of the 6 gaps for the A's can be done in 6C2 = 15 ways, so multiplying 60 by 15 gives 900.