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# Let each different arrangement of all the letters of DELETED

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Manager
Joined: 17 Mar 2010
Posts: 156
Let each different arrangement of all the letters of DELETED [#permalink]

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20 May 2010, 23:32
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100% (00:33) correct 0% (00:00) wrong based on 7 sessions

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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?

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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Joined: 02 Sep 2009
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21 May 2010, 00:08
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: $$\frac{7!}{2!3!}-\frac{6!}{3!}=300$$.

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

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16 Sep 2017, 23:07
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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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