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Re: Permuation Problem [#permalink]
26 Mar 2008, 16:51
3
This post received KUDOS
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
Re: Permuation Problem [#permalink]
24 Mar 2010, 18:51
1
This post received KUDOS
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
Re: Permuation Problem [#permalink]
25 Mar 2010, 02:27
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? _________________
"Don't be afraid of the space between your dreams and reality. If you can dream it, you can make it so." Target=780 http://challengemba.blogspot.com Kudos??
Re: Permuation Problem [#permalink]
25 Mar 2010, 04:34
2
This post received KUDOS
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 Options P _ _ _ _ S _ _ _ _ _ _
_ P _ _ _ _ S _ _ _ _ _
_ _ P _ _ _ _ S _ _ _ _
_ _ _ P _ _ _ _ S _ _ _
. . . . . _ _ _ _ _ _ P _ _ _ _ S
You can fill the reamining blanks with anyof the letters.
Re: Permuation Problem [#permalink]
25 Mar 2010, 08:32
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 Options P _ _ _ _ S _ _ _ _ _ _
_ P _ _ _ _ S _ _ _ _ _
_ _ P _ _ _ _ S _ _ _ _
_ _ _ P _ _ _ _ S _ _ _
. . . . . _ _ _ _ _ _ P _ _ _ _ S
You can fill the reamining blanks with anyof the letters.
Thanks
Ravi
Thanks! man. kudos _________________
"Don't be afraid of the space between your dreams and reality. If you can dream it, you can make it so." Target=780 http://challengemba.blogspot.com Kudos??
Re: In how many ways can the letters of the word PERMUTATIONS be [#permalink]
10 Nov 2013, 02:30
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Permutations of \(n\) things of which \(P_1\) are alike of one kind, \(P_2\) are alike of second kind, \(P_3\) are alike of third kind ... \(P_r\) are alike of \(r_{th}\) kind such that: \(P_1+P_2+P_3+..+P_r=n\) is:
\(\frac{n!}{P_1!*P_2!*P_3!*...*P_r!}\).
For example number of permutation of the letters of the word "gmatclub" is 8! as there are 8 DISTINCT letters in this word.
Number of permutation of the letters of the word "google" is \(\frac{6!}{2!2!}\), as there are 6 letters out of which "g" and "o" are represented twice.
Number of permutation of 9 balls out of which 4 are red, 3 green and 2 blue, would be \(\frac{9!}{4!3!2!}\).
Back to the original questions:
In how many ways can the letters of the word PERMUTATIONS be arranged if there are always 4 letters between P and S?
There are 12 letters in the word "PERMUTATIONS", out of which T is repeated twice.
1. Choosing 4 letters out of 10 (12-2(P and S)=10) to place between P and S = 10C4 = 210; 2. Permutation of the letters P ans S (PXXXXS or SXXXXP) = 2! =2; 3. Permutation of the 4 letters between P and S = 4! =24; 4. Permutations of the 7 units {P(S)XXXXS(P)}{X}{X}{X}{X}{X}{X} = 7! = 5040; 5. We should divide multiplication of the above 4 numbers by 2! as there is repeated T.
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