# CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

###### CAT Questions | Permutation Probability | Rearrangement of Letters CAT Questions

The question is from Permutation and Combination. This is about Rearrangement of Letters. Our task is to find the probability of a word satisfying particular condition. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 18: If all the rearrangements of the word AMAZON are considered, what is the probability that M will feature between the 2As?

1. $$frac{1}{3}\\$ 2. $\frac{1}{6}\\$ 3. $\frac{2}{5}\\$ 4. $\frac{3}{8}\\$ ## 🎉Get Upto ₹6,000 off on our CAT 2024 and IPM 2024/25 courses! Valid till 1st December 2023.★ Register now ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Permutation and Combination: If you know the different rearrangements of letters in the given word, you are through!! For this type of question, we need to consider only the internal arrangement within the M and 2As. M and 2As can be rearranged as AMA, AAM, or MAA. So, the probability that M will feature between the 2As is $\frac{1}{3}\\$. Now, let us think why we need to consider only the M and 2As. Let us start by considering a set of words where the M and 2 As are placed at positions 2, 3 and 5. The other three letters have to be in slots 1, 4 and 6 Three letters can be placed in three different slots in 3! = 6 ways. Now with __ M A __ A __ there are 6 different words. With __ A M __ A __ there are 6 different words. With __ A A __ M __ there are 6 different words. For each selection of the positions for A,A and M, exactly one-third of words will have M between the two A’s. This is why only the internal arrangement between A, A and M matters. So, probability of M being between 2 As is $\frac{1}{3}\\$. The question is "what is the probability that M will feature between the 2As?" ##### Hence the answer is "$\frac{1}{3}\\$" Choice A is the correct answer. ###### 🎉Get Upto ₹6,000 off on our CAT 2024 and IPM 2024/25 courses! Valid till 1st December 2023. ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Preparation Online | CAT Permutation and Combination; Probability Videos On YouTube #### Other useful sources for Permutation and Combination Questions | Probability Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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