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chillpill
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In how many ways can the letters of the word ARRANGE be 12 Apr 2006, 20:12
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In how many ways can the letters of the word ARRANGE be rearranged so that neither the two Rs nor the two As can come together?



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In how many ways can the letters of the word ARRANGE be 12 Apr 2006, 21:48
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chillpill
In how many ways can the letters of the word ARRANGE be rearranged so that neither the two Rs nor the two As can come together?
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I'm guessing is: 7! - 2*6! - 5! = 3480

7! number of ways to arrange a word with the letters A-R-R-A-N-G-E

let's make AA = A and
RR = R

then we can have A-R-R-N-G-E
or A-R-A-N-G-E

in 6! ways

and A-R-N-G-E in 5! ways
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Professor
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In how many ways can the letters of the word ARRANGE be 12 Apr 2006, 21:54
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conocieur
chillpill
In how many ways can the letters of the word ARRANGE be rearranged so that neither the two Rs nor the two As can come together?

I'm guessing is: 7! - 2*6! - 5! = 3480

7! number of ways to arrange a word with the letters A-R-R-A-N-G-E

let's make AA = A and
RR = R

then we can have A-R-R-N-G-E
or A-R-A-N-G-E

in 6! ways

and A-R-N-G-E in 5! ways
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A-R-R-A-N-G-E

i think we can AA togather in 2 (6) x 5! ways = 2x6! ways.
similarly RR can also be done in the same way but i guess RR already comes in AA's arrangements.... so :roll: :roll: :roll: :roll:
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In how many ways can the letters of the word ARRANGE be 12 Apr 2006, 22:17
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Here is my shot at it...

Total - {2Rs together + 2As together - RRAA all of them together}
.. beacuse both the cases where 2Rs/2As are together also include RRAA. We need to subtract those... Sort of Venn diagram problem
= 7!/(2!*2!) - {(2*6!/2!) - 5! }
= 660

OA please?
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In how many ways can the letters of the word ARRANGE be 12 Apr 2006, 22:24
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giddi77
Here is my shot at it...

Total - {2Rs together + 2As together - RRAA all of them together}
.. beacuse both the cases where 2Rs/2As are together also include RRAA. We need to subtract those... Sort of Venn diagram problem
= 7!/(2!*2!) - {(2*6!/2!) - 5! }
= 660

OA please?
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but remember AA ( or RR) can placed in two ways.. for AA, lets say Aa; we can put Aa two ways. so you are missing 2.

confusing..... :oops:
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chillpill
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In how many ways can the letters of the word ARRANGE be 13 Apr 2006, 01:16
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giddi77
Here is my shot at it...

Total - {2Rs together + 2As together - RRAA all of them together}
.. beacuse both the cases where 2Rs/2As are together also include RRAA. We need to subtract those... Sort of Venn diagram problem
= 7!/(2!*2!) - {(2*6!/2!) - 5! }
= 660

OA please?
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yeah yeah yeah this is correct. thanks



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
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