the consonants appear

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Apr 05, 2011 4:17 am

What is the probability that the position in which the consonants appear remain unchanged when the letters of the word MATH are re-arranged?
(A) 1/24
(B) 1/12
(C) 1/6
(D) 1/4
(E) 1/3

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Source: Beat The GMAT — Problem Solving | Tue Apr 05, 2011 4:17 am

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Tue Apr 05, 2011 4:19 am

(A) 1/24 ?

Ways of arranging 4!
Only case of consonants remaining is same place is the word MATH.

Vineesh,
Just telling you what I know and think. I am not the expert.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Apr 05, 2011 4:21 am

vineeshp wrote:(A) 1/24 ?

Ways of arranging 4!
Only case of consonants remaining is same place is the word MATH.

sorry

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Apr 05, 2011 4:53 am

sanju09 wrote:What is the probability that the position in which the consonants appear remain unchanged when the letters of the word MATH are re-arranged?
(A) 1/24
(B) 1/12
(C) 1/6
(D) 1/4
(E) 1/3

There are 4 letters in the word "MATH", which can be arranged in 4! = 24 ways.
The consonants M, T, and H can be re-arranged in 3! = 6 ways (the consonants can only take the 1st, 3rd, and 4th place)
Hence, the required probability = 6/24 = 1/4

The correct answer is D.

Last edited by Anurag@Gurome on Tue Apr 05, 2011 5:02 am, edited 1 time in total.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Apr 05, 2011 5:00 am

Anurag@Gurome wrote:
sanju09 wrote:What is the probability that the position in which the consonants appear remain unchanged when the letters of the word MATH are re-arranged?
(A) 1/24
(B) 1/12
(C) 1/6
(D) 1/4
(E) 1/3
There are 4 letters in the word "MATH", which can be arranged in 4! = 24 ways.
The consonants M, T, and H can be re-arranged in 3! = 6 ways (the consonants can only take the 1st, 2nd, and 3rd place)
Hence, the required probability = 6/24 = 1/4

The correct answer is D.

Very correct, EXCEPT the consonants can take 2nd place.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Apr 05, 2011 5:02 am

sanju09 wrote:
Anurag@Gurome wrote:
sanju09 wrote:What is the probability that the position in which the consonants appear remain unchanged when the letters of the word MATH are re-arranged?
(A) 1/24
(B) 1/12
(C) 1/6
(D) 1/4
(E) 1/3
There are 4 letters in the word "MATH", which can be arranged in 4! = 24 ways.
The consonants M, T, and H can be re-arranged in 3! = 6 ways (the consonants can only take the 1st, 2nd, and 3rd place)
Hence, the required probability = 6/24 = 1/4

The correct answer is D.
Very correct, EXCEPT the consonants can take 2nd place.

Thanks for pointing the typo Sanju, edited the previous post.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Apr 05, 2011 10:22 am

sanju09 wrote:What is the probability that the position in which the consonants appear remain unchanged when the letters of the word MATH are re-arranged?
(A) 1/24
(B) 1/12
(C) 1/6
(D) 1/4
(E) 1/3

Question rephrased: What is the probability that A appears in the 2nd position?

There are 4 positions in which A could appear.
Thus, P(A in 2nd position) = 1/4.

The correct answer is D.

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force5: Legendary Member; Posts: 582; Joined: Tue Mar 08, 2011 12:48 amFollowed by: 6 members; Thanked: 61 times; GMAT Score:740

by force5 » Wed Apr 06, 2011 12:44 am

Good question sanju09 and awesome reply anurag and specially mitch.

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rohit56: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Sat Dec 15, 2018 12:06 am

by rohit56 » Mon Dec 17, 2018 10:04 pm

If we have to consolidate the position for consonants then consonants will appear at first , third and fourth position while vowel will appear at second position.
No of ways of arranging consonants on these positions = 3! = 6 ways.
Total no of ways of arranging letters of word 'MATH' without restrictions = 4! = 24
So probability = 6/24 = 1/4

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