GMAT Probability Practice Question 3

Rearrangement & Reordering | GMAT Sample Questions

This Free GMAT quant practice question is an easy problem solving question in probability. The concept tested in this question is to find the probability that consonants in a word appear in a specified sequence when letters of the word are rearranged.

Question 3: 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})

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Explanatory Answer | GMAT Probability | Reordering

Step 1 of solving this GMAT Probability Question: Compute the 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.

Step 2 of solving this GMAT Probability Question: 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.
In all of these rearrangements, 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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