The GMAT Sample Math question is a probability problem solving question. The concept tested in this question is to find the probability of a particular sequence when letters of a word are rearranged.
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
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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