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How many ways can the letters in the word COMMON be arranged

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How many ways can the letters in the word COMMON be arranged [#permalink]

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New post 22 Feb 2013, 08:21
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How many ways can the letters in the word COMMON be arranged?

A. 6
B. 30
C. 90
D. 120
E. 180

[Reveal] Spoiler: How to solve
This is a permutation with indistinguishable events - repeated items. The number of different permutations of N objects, where there are N1 indistinguishable objects of style 1, N2 indistinguishable objects of style 2, ..., and Nk indistinguishable objects of style k, is = N!/(N1!*N2!* ... * Nk!). In this case, N=6; N1=2, and N2=2. This gives the formula: 6!/(2!*2!)=180
[Reveal] Spoiler: OA
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Re: How many ways can the letters in the word COMMON be arranged [#permalink]

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New post 22 Feb 2013, 08:28
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johnwesley wrote:
How many ways can the letters in the word COMMON be arranged?

A. 6
B. 30
C. 90
D. 120
E. 180

[Reveal] Spoiler: How to solve
This is a permutation with indistinguishable events - repeated items. The number of different permutations of N objects, where there are N1 indistinguishable objects of style 1, N2 indistinguishable objects of style 2, ..., and Nk indistinguishable objects of style k, is = N!/(N1!*N2!* ... * Nk!). In this case, N=6; N1=2, and N2=2. This gives the formula: 6!/(2!*2!)=180


THEORY FOR SUCH KIND OF PERMUTATION QUESTIONS:

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 QUESTION:
How many ways can the letters in the word COMMON be arranged?
A. 6
B. 30
C. 90
D. 120
E. 180

According to the above the # of permutations of 6 letters COMMON out of which 2 O's and 2 M's are identical is \(\frac{6!}{2!*2!}=180\).

Answer: E.

Hope it's clear.
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Re: How many ways can the letters in the word COMMON be arranged [#permalink]

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New post 08 Feb 2015, 05:17
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Re: How many ways can the letters in the word COMMON be arranged [#permalink]

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New post 05 Apr 2016, 09:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many ways can the letters in the word COMMON be arranged   [#permalink] 05 Apr 2016, 09:09
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