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Probability - November 26, 2004
The GMAT Sample Math question for the day is from the topic Probability.
Question
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. 1/4
B. 1/6
C. 1/3
D. 1/24
E. 1/12
The correct choice is (A) and the correct answer is 1/4.
Explanatory Answer
The total number of ways in which the word Math can be re-arranged = 4! = 4*3*2*1 = 24 ways.
Now, if the positions in which the consonants appear do not change, the first, third and the fourth positions are reserved for consonants and the vowel A remains at the second position.
The consonants M, T and H can be re-arranged in the first, third and fourth positions in 3! = 6 ways without the positions in which the positions in which the consonants appear changing.
Therefore, the required probability =
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