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# There are 6 letters and 2 of them are the same. How many

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Senior Manager
Joined: 08 Aug 2005
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There are 6 letters and 2 of them are the same. How many [#permalink]

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06 May 2006, 05:09
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

There are 6 letters and 2 of them are the same. How many ways can depart the 2 same letters with at least 1 other letter?

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VP
Joined: 29 Dec 2005
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10 May 2006, 22:08
getzgetzu wrote:
There are 6 letters and 2 of them are the same. How many ways can depart the 2 same letters with at least 1 other letter?

= 4c1+4c2+4c3+4c4

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GMAT Club Legend
Joined: 07 Jul 2004
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10 May 2006, 22:22
Just work around with the 4 letters.

Total number of ways = 4C1 + 4C2 + 4C3 + 4C4 = 4 + 6 + 4 + 1 = 15 ways

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Intern
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10 May 2006, 22:23
2c2*(4 c 1+4 c 2+4 c 3+4 c 4) = 15.
_________________

If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut.
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Director
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10 May 2006, 22:25
I will give it a hand,
6 letters , 2 same, can be arranged in 6!/2 different ways. When 2 are together in 5! different ways. Then the ans should be 6!/2-5!=240 ways when there wil be AT LEAST one letter in between.

Prof, i think that you select the letters out of the remaining 4 different but shouldn't the permutations of these selections be considered?

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GMAT Club Legend
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10 May 2006, 22:30
BG wrote:
I will give it a hand,
6 letters , 2 same, can be arranged in 6!/2 different ways. When 2 are together in 5! different ways. Then the ans should be 6!/2-5!=240 ways when there wil be AT LEAST one letter in between.

Prof, i think that you select the letters out of the remaining 4 different but shouldn't the permutations of these selections be considered?

We should use combinations and not permutations. This is because which letter is arranged first has no meaning to the solution. We're only interested in what is inside a group of letters selected.

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10 May 2006, 22:30
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