Re: How many ways can you arrange the word "ARRANGE"
In this case we need to arrange the letters with the condition that two R's do not come together.
It is easy to find the number of words the two R's come together.
Let us find the total number of different words that can be formed with the letters in "ARRANGE". then it is easy find number of words two R's do not come together.
The word "ARRANGE" has two repeated elements A(twice) and R(twice). The formula for permutations with repeated elements is as follows,
When k out of n elements are indistinguishable, e.g. k copies of the same book, the number of different permutations is n!/k!.
Therefore the total number of different words that can be formed is 7!/2! *2!
To find the number of words the two R's come together let us consider the pair RR as one single element and now we have six elements with one repeated element "A".
Therefore the total number of different words with two R's come together is 6!/2!
Hence number of words that two R's don't come together is
7!/2! *2! - 6!/2! = 1260 -360 = 900
Actually I was wrong in my previous post. I did not notice that the word has two A's.
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