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In how many ways can the letters in PRECISION be arranged?

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In how many ways can the letters in PRECISION be arranged? [#permalink] New post 23 Feb 2010, 14:39
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In how many ways can the letters in PRECISION be arranged? In how many of these arrangements do the vowels occupy even places ?


[Reveal] Spoiler:
IMO:
No of letters in PRECISION = 9
No of ways the letters in PRECISION can be arranged = 9!/2! = 181440

No of vowels in the word PRECISION = 4
No of even spaces in the word PRECISION = 4
Vowels in even spaces = 4C4
Remaining num of letters = 5P5
4C4*5P5=120
Actual answer =
[Reveal] Spoiler:
1440
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Re: Permutation question [#permalink] New post 23 Feb 2010, 14:54
Expert's post
jazzyqueen wrote:
In how many ways can the letters in PRECISION be arranged? In how many of these arrangements do the vowels occupy even places ?
IMO:
No of letters in PRECISION = 9
No of ways the letters in PRECISION can be arranged = 9!/2! = 181440

No of vowels in the word PRECISION = 4
No of even spaces in the word PRECISION = 4
Vowels in even spaces = 4C4
Remaining num of letters = 5P5
4C4*5P5=120
Actual answer =
[Reveal] Spoiler:
1440


Welcome to Gmat Club jazzyqueen.

Question #2:
4 vowels out of which two are identical can be arranged in even places in 4!/2!=12 # of ways.
Remaining 5 letters can be arranged in 5!=120 # of ways.

Total 12*120=1440.
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Re: Permutation question [#permalink] New post 25 Feb 2010, 04:19
Bunuel wrote:
jazzyqueen wrote:
In how many ways can the letters in PRECISION be arranged? In how many of these arrangements do the vowels occupy even places ?
IMO:
No of letters in PRECISION = 9
No of ways the letters in PRECISION can be arranged = 9!/2! = 181440

No of vowels in the word PRECISION = 4
No of even spaces in the word PRECISION = 4
Vowels in even spaces = 4C4
Remaining num of letters = 5P5
4C4*5P5=120
Actual answer =
[Reveal] Spoiler:
1440


Welcome to Gmat Club jazzyqueen.

Question #2:
4 vowels out of which two are identical can be arranged in even places in 4!/2!=12 # of ways.
Remaining 5 letters can be arranged in 5!=120 # of ways.

Total 12*120=1440.



not sure, but I think 1440 in both case if we start with Vowels and non-Vowels, so I think we need to divid by 2.
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Re: Permutation question [#permalink] New post 26 Feb 2010, 11:47
In how many ways can the letters in PRECISION be arranged? In how many of these arrangements do the vowels occupy even places ?
IMO:
No of letters in PRECISION = 9
No of ways the letters in PRECISION can be arranged = 9!/2! = 181440

No of vowels in the word PRECISION = 4
No of even spaces in the word PRECISION = 4
Vowels in even spaces = 4C4
Remaining num of letters = 5P5
4C4*5P5=120

-------------------------

4 vowels with I repeated.
Number of ways 4 vowels can occupy 4 even spaces = 4P4 / 2! (as I is repeated) = 12
Number of ways 5 consonants can occupy 5 odd spaces = 5P5 = 120

Therefore total number of ways = 12 * 120 = 1440
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Re: Permutation question   [#permalink] 26 Feb 2010, 11:47
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