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# A Question on permutations. Will appreciate if you can answer it fast

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Find the number of ways in which letters of the word ARRANGEMENT can be arranged so that the two A‟s and two R‟s do not occur together.

Guest Oct 14, 2017
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#1
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Find the number of ways in which letters of the word ARRANGEMENT can be arranged so that the two A‟s and two R‟s do not occur together.

AA RR NN EE G M T

I'm going to think of this as  AR NN EE G M T

How many distict ways can this be arranged.  I have treated AA and RR as just one item each.

So I think this is how many ways the letters can be arranged so that the 2Rs and 2As are together.

$$\frac{9!}{2!2!}=\frac{9!}{4}$$   ways

Now how many ways can the original set be arranged.

$$\frac{11!}{2!2!2!2!}= \frac{11! }{16}$$

So the number of ways that the 2As and the 2Rs are not together is

$$\frac{11!}{16}-\frac{9!}{4}=2494800-90720 = 2402080$$

I think.

Melody  Oct 14, 2017
#2
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If you asked this question Jeff123 it is better that you stay anonymous.

You are not polite enough to be a proper member of this forum.

If it was not Jeff and you are polite then it would be nice if you joined up.

That way you can track your questions much more easily and you get email notification when answers are given :)

If you get known as a polite participant of the forum answerers will give you are great deal of help and attention. :)

Melody  Oct 14, 2017

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