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Let each different arrangement of all the letters of DELETED

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Let each different arrangement of all the letters of DELETED [#permalink]

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New post 20 May 2010, 23:32
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Let each different arrangement of all the letters of DELETED be called a word. In how many of these words will the D's be separated?

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I am getting answer as 300. Can someone please explain if the answer is correct? I am not sure if wee need to carry out some operation because of repetation of D's.

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Re: Permutations [#permalink]

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New post 21 May 2010, 00:08
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amitjash wrote:
Let each different arrangement of all the letters of DELETED be called a word. In how many of these words will the D's be separated?

I am getting answer as 300. Can someone please explain if the answer is correct? I am not sure if wee need to carry out some operation because of repetation of D's.


There are 7 letters in the word "DELETED", out of which: D=2, E=3, L=1, T=1.

Total # of permutations is \(\frac{7!}{2!3!}=420\);
# of permutations with D's together is \(\frac{6!}{3!}=120\). Consider 2 D's as one unit: {DD}{E}{E}{E}{L}{T} - total 6 units, out of which {DD}=1, {E}=3, {L}=1, {T}=1.

# of permutations with D's not come together is: \(\frac{7!}{2!3!}-\frac{6!}{3!}=300\).

So your answer is correct.

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Re: Let each different arrangement of all the letters of DELETED [#permalink]

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New post 24 Jul 2016, 08:54
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Re: Let each different arrangement of all the letters of DELETED [#permalink]

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New post 16 Sep 2017, 23:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Let each different arrangement of all the letters of DELETED   [#permalink] 16 Sep 2017, 23:07
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