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

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Joined: 24 Jan 2013
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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
1
8
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

78% (00:43) correct 22% (01:23) wrong based on 236 sessions

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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

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
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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
7
5
johnwesley wrote:
How many ways can the letters in the word COMMON be arranged?

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

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 02 Jun 2019, 02:15
1
johnwesley wrote:
How many ways can the letters in the word COMMON be arranged?

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

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


total possible ways
6!/2!*2! = 180
IMO E
GMAT Club Bot
Re: How many ways can the letters in the word COMMON be arranged   [#permalink] 02 Jun 2019, 02:15
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