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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the consonants appear
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sanju09
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sanju09
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sorryvineeshp wrote:(A) 1/24 ?
Ways of arranging 4!
Only case of consonants remaining is same place is the word MATH.
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Anurag@Gurome
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There are 4 letters in the word "MATH", which can be arranged in 4! = 24 ways.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
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
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Very correct, EXCEPT the consonants can take 2nd place.Anurag@Gurome wrote:There are 4 letters in the word "MATH", which can be arranged in 4! = 24 ways.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
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.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
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Anurag@Gurome
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Thanks for pointing the typo Sanju, edited the previous post.sanju09 wrote:Very correct, EXCEPT the consonants can take 2nd place.Anurag@Gurome wrote:There are 4 letters in the word "MATH", which can be arranged in 4! = 24 ways.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
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.
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Question rephrased: What is the probability that A appears in the 2nd position?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 positions in which A could appear.
Thus, P(A in 2nd position) = 1/4.
The correct answer is D.
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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
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
