Introduction:
The word 'arrange' has 7 letters. We have to find out the number of ways in which the letters can be arranged such that the two R's do not come together.

Step 1:
Firstly, we will find the total number of ways in which the letters of the word 'arrange' can be arranged.

Since the word has 7 letters, the total number of ways in which the letters can be arranged is 7! = 5040.

Step 2:
Next, we will find the number of ways in which the two R's can come together.

If we consider the two R's as a single letter, then we have 6 letters to arrange.

The number of ways in which these letters can be arranged is 6! = 720.

However, since the two R's can be arranged in 2! = 2 ways, we need to multiply the above result by 2.

Therefore, the number of ways in which the two R's can come together is 2 x 6! = 1440.

Step 3:
Finally, we will subtract the number of ways in which the two R's can come together from the total number of ways in which the letters can be arranged to get the number of ways in which the two R's do not come together.

Number of ways in which the two R's do not come together = Total number of ways - Number of ways in which the two R's can come together

= 5040 - 1440

= 3600.

Conclusion:
Therefore, the number of ways in which the letters of the word 'arrange' can be arranged such that the two R's do not come together is 3600.

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