# GMAT® Quant Practice : Probability

Concept: Rearranging letters of a word. Basics of probability.

This GMAT quant practice question is a problem solving question in probability. The concept tested in this question is to find the probability that a specific sequence occurs when letters of a word are rearranged.

#### 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?

1. $\frac{1}{4}\\$
2. $\frac{1}{6}\\$
3. $\frac{1}{3}\\$
4. $\frac{1}{24}\\$
5. $\frac{1}{12}\\$

#### Compute denominator

In any probability question, the denominator represents the total number of outcomes for an event. The numerator represents the number of favorable outcomes.

The total number of ways in which the letters of the word MATH can be re-arranged = 4! = 4*3*2*1 = 24 ways.

#### Compute numerator and the probability

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 so that the positions in which the consonants appear remain unchanged.

Therefore, the required probability $\frac{6}{24} = \frac{1}{4}\\$

Choice A is the correct answer.

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