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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] New post 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] New post 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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 [#permalink] New post 10 May 2006, 21:22
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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 [#permalink] New post 10 May 2006, 21:23
2c2*(4 c 1+4 c 2+4 c 3+4 c 4) = 15.
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 [#permalink] New post 10 May 2006, 21:25
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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 [#permalink] New post 10 May 2006, 21:30
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.
  [#permalink] 10 May 2006, 21:30
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There are 6 letters and 2 of them are the same. How many

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