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

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Senior Manager
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There are 6 letters and 2 of them are the same. How many [#permalink]  06 May 2006, 04:09
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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Re: letters [#permalink]  10 May 2006, 21:08
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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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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2c2*(4 c 1+4 c 2+4 c 3+4 c 4) = 15.
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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?
GMAT Club Legend
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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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