# Number of ways the letters of “Arrange” can be arranged so that the two r's are not consecutive [closed]

Show that the number of ways in which the letters of the word "arrange" can be arranged so that the two r's are not consecutive is $900$.

## closed as off-topic by Ian Miller, Namaste, Ken Duna, draks ..., hardmathMar 14 '17 at 16:47

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• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Ian Miller, Namaste, Ken Duna, hardmath
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• Possible duplicate of Arrangement of word MISSISSIPPI in which no three S occur together – HSN Mar 14 '17 at 9:38
• Hi, welcome to Math.SE. Please indicate what you have tried, your thoughts on the problem and where you got stuck. This will help people better tailor their answer to your background and situation. It will also demonstrate that you are interested in your question and not just looking for someone to do your homework for you - Math.SE is not a homework site. – Ian Miller Mar 14 '17 at 9:41
• In the title the word "Arrange" is capitalized, but not in the body of your Question. This might lead to different interpretations of the problem accordingly as the two letters $A,a$ are considered identical or distinguishable. – hardmath Mar 14 '17 at 16:46

1. Number of arrangements of AANGE is $\frac{5!}{2!}=60$
2. In every arrangement of AANGE we can select two different positions where to put additional R in ${6 \choose 2}=15$ ways
3. Number of our arrangemenst of ARRANGE without consecutive Rs is then $60\cdot 15=900$