Rearrange REARRANGE!

Hi, I have some questions to ask you (which in fact, I don't know the answer).

I found some questions in the exam which they ask like "How many ways to rearrange "PERMUTATION" in a line without having N, P, and I sitting next to each other?". This question seems to be not difficult to solve. However, when I look at the solution and think about this question again, I found another question which is hard to solve (for me).

How many ways to rearrange "REARRANGE" in a line without having the same letter sitting next to each other? For example, REARARNGE is correct but RREARANGE is wrong.

Could you discuss about the solution and the method you would use in order to solve this question?

#Combinatorics

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$