Number of ways the letters of "Arrange" can be arranged so that the two r's are not consecutive

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  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 $60\cdot 15=900$
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sophin
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sophin

I'm a junior android developer coding with Kotlin to develop android application. Java Programming language was the first language I learned, as I know much more about java programming language compare to Kotlin. But as Kotlin is considered android official language to developed android app by google. Over my past experience, I have learned JavaScript, Dart. I started my programming journey when I was 18 years old. During that journey, I have built simple 2D games with the help of Game Maker Studio, create Messaging App with the help of Messaging API, worked on JSON, REST API client, awt, swing, util, applet and Recycler View. Weather App, Grocery App, Music App, Messaging App, Location Finder, Browser, are a few examples of an app I created.

Updated on August 01, 2022

Comments

  • sophin
    sophin over 1 year

    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 $900$.

    • HSN
      HSN over 6 years
    • Ian Miller
      Ian Miller over 6 years
      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.
    • hardmath
      hardmath over 6 years
      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.