# 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. $\frac{1}{12}$ ## Get to Q51 in GMAT Quant #### Online GMAT Course From INR 3000 ### Video Explanation ## GMAT Live Online Classes #### Starts Thu, Dec 14, 2023 ### 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. #### GMAT Online CourseTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GMAT Live Online Classes Next Batch Dec 14, 2023 ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 95000 48484
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