Find the number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together.

The word ARRANGE has 7 letters, with the letters A and R each repeating twice, so the total unrestricted arrangements are calculated using the formula for permutations with repetition. The total arrangements are 7! divided by (2! times 2!), which equals 5040 divided by 4, or 1260. To find the arrangements where the two R's are together, treat them as a single unit, which gives 6 units to arrange with A repeating twice, yielding 6! divided by 2!, or 360. Subtracting the arrangements where R's are together from the total gives 1260 minus 360, which equals 900. The result is 900.

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