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In how many ways can the letters of the word PERMUTATIONS be [#permalink]
 26 Mar 2008, 17:13
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In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
OA is 25401600.
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Re: Permuation Problem [#permalink]
26 Mar 2008, 17:51
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I figured out the solution however it is not a simple permutation question. This includes both permutation as well as combination.
There are 12 words in letter PERMUTATIONS. Out of which T is repeated twice.
Now first we need to see how many ways we can make word with 4 letter between P and S.
Except P and S there are total of 10 letters, so number of way of selecting them = 10C4 = 210
Also note that question is asking to place exactly 4 words between P and S, but does not tells you if P has to be the first letter of S has to be the first letter. So In all the above combinations, we can rotate the position of P and S.
So total way = 210*2 = 420
The selected 4 letters can be rotated between P and S in = 4! ways
So total ways = 420 * 4!
Consider this 6 letter chunk (P, S, and 4 letter between them) as 1 letter.
Remaining letters are 6. So in total we have 7 letters, which can be arranged in 7! ways.
So total number of ways = 7! * 420 * 4!
Now since letter T was repeated twice, we should divide the above result by 2!.
So Total number of ways = 7! * 420 * 4! / 2! = 25401600
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Re: Permuation Problem [#permalink]
24 Mar 2010, 19:51
Same answer but a slightly different approach.
In the 12 letter word there are 14 different positions (1,6 2,7 3,8 4,9 5,10 6,11 7,12 and reverse) where P and S can be separated by 4 letters. Now the remaining 10 letters can be ordered in 10!/2! ways since T repeats twice.
So total no of ways PERMUTATIONS be arranged so that there are 4 letters between P and S is
14*10!/2! = 25401600
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Re: Permuation Problem [#permalink]
25 Mar 2010, 03:27
crack700 wrote: Same answer but a slightly different approach.
In the 12 letter word there are 14 different positions (1,6 2,7 3,8 4,9 5,10 6,11 7,12 and reverse) where P and S can be separated by 4 letters. Now the remaining 10 letters can be ordered in 10!/2! ways since T repeats twice.
So total no of ways PERMUTATIONS be arranged so that there are 4 letters between P and S is
14*10!/2! = 25401600 Sorry! didn't get the red part. Please! can you explain it a bit more?
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Re: Permuation Problem [#permalink]
25 Mar 2010, 05:34
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AtifS wrote: crack700 wrote: Same answer but a slightly different approach.
In the 12 letter word there are 14 different positions (1,6 2,7 3,8 4,9 5,10 6,11 7,12 and reverse) where P and S can be separated by 4 letters. Now the remaining 10 letters can be ordered in 10!/2! ways since T repeats twice.
So total no of ways PERMUTATIONS be arranged so that there are 4 letters between P and S is
14*10!/2! = 25401600 Sorry! didn't get the red part. Please! can you explain it a bit more? If you start putting in "P" & "S" first you can put them in the following patterns Total 14 OptionsP _ _ _ _ S _ _ _ _ _ _ _ P _ _ _ _ S _ _ _ _ _ _ _ P _ _ _ _ S _ _ _ _ _ _ _ P _ _ _ _ S _ _ _ . . . . . _ _ _ _ _ _ P _ _ _ _ S You can fill the reamining blanks with anyof the letters. Thanks Ravi
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Re: Permuation Problem [#permalink]
25 Mar 2010, 09:32
sudgmat wrote: AtifS wrote: crack700 wrote: Same answer but a slightly different approach.
In the 12 letter word there are 14 different positions (1,6 2,7 3,8 4,9 5,10 6,11 7,12 and reverse) where P and S can be separated by 4 letters. Now the remaining 10 letters can be ordered in 10!/2! ways since T repeats twice.
So total no of ways PERMUTATIONS be arranged so that there are 4 letters between P and S is
14*10!/2! = 25401600 Sorry! didn't get the red part. Please! can you explain it a bit more? If you start putting in "P" & "S" first you can put them in the following patterns Total 14 OptionsP _ _ _ _ S _ _ _ _ _ _ _ P _ _ _ _ S _ _ _ _ _ _ _ P _ _ _ _ S _ _ _ _ _ _ _ P _ _ _ _ S _ _ _ . . . . . _ _ _ _ _ _ P _ _ _ _ S You can fill the reamining blanks with anyof the letters. Thanks Ravi Thanks! man. kudos
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Re: Permuation Problem
[#permalink]
25 Mar 2010, 09:32
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