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# The letters of word "SOCIETY" are placed at random in a row. The proba

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
The letters of word "SOCIETY" are placed at random in a row. The proba  [#permalink]

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28 Jan 2019, 05:57
1
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Difficulty:

45% (medium)

Question Stats:

64% (01:53) correct 36% (01:47) wrong based on 33 sessions

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The letters of word "SOCIETY" are placed at random in a row. The probability that three vowels come together, is:

A. 6/7
B. 5/7
C. 4/7
D. 3/7
E. 1/7

The word " S O C I E T Y " is to be arranged in a row what is the probability that the vowels come together

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The letters of word "SOCIETY" are placed at random in a row. The proba  [#permalink]

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28 Jan 2019, 06:11
Lets first take care of the denominator The letters of word "SOCIETY can be arranged in 7! ways.
Numerator : lets get them all vowels together OIE and others SCTY. lets keep them vowels togethe, so then, if we name vowels as V we get, VSCTY which can be arranged in 5! and the vowels can be arranged within themselves in 3! ways. Altogether, we get $$\frac{5!3!}{7!}$$ which reduces to $$\frac{1}{7}$$
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Joined: 23 Oct 2013
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Re: The letters of word "SOCIETY" are placed at random in a row. The proba  [#permalink]

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28 Jan 2019, 06:19
consider o,i,e as 1 unit so total 5 units s,c,t,y and(o,i,e) can br arranged in 5!*3!(3! for arranging o,i,e)

so 5!*3!/7!=1/7
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Re: The letters of word "SOCIETY" are placed at random in a row. The proba  [#permalink]

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28 Jan 2019, 07:01
Bunuel wrote:
The letters of word "SOCIETY" are placed at random in a row. The probability that three vowels come together, is:

A. 6/7
B. 5/7
C. 4/7
D. 3/7
E. 1/7

The word " S O C I E T Y " is to be arranged in a row what is the probability that the vowels come together

total arrangements possible 7!

vowels : OIE = 3!
XSCTY
it can be arranged in 5! ways
so 5!* 3! /7! = 1/7
IMO E
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Re: The letters of word "SOCIETY" are placed at random in a row. The proba   [#permalink] 28 Jan 2019, 07:01
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