How many ways can you arrange the word "ARRANGE"

How many ways can you arrange the word "ARRANGE". But the condition is the two R's do not come together..

Ans is 1,800 diff ways.

7!/2! - 6! = 1800

Hi James,

Can you please explain which formula you have been used..I am confused. I know only one formula:
Find all of the differennt ways to arrange "r" items out of "n" items.
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suresh

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.

ok thanks james...
now i'm also cleared about that doubt..
i thought suresh also now cleared..
thanks a lot..