# CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

###### CAT Questions | Permutation Probability | Letters Rearrangment
CAT Questions

The question is from Permutation and Combination. This question is about Letters Rearrangment. We need to find out the number of ways the letters can be rearranged from a particular word with a condition given. 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 30: In how many ways can we rearrange the letters of the word MANANA such that no two A’s are adjacent to each other?

1. 3 ! * 5C3
2. 4 ! * 4C3
3. 3 * 4C3
4. 3 ! * 4C3

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##### Method of solving this CAT Question from Permutation and Combination: Simple Rearrangment Question!!

MANANA has 6 letters, of which 3 are A's
Now, let us place the letters that are not As on a straight line. We have MNN. These can be arranged in $$frac{3!}{2!}\\$ = 3 ways. Now let us create slots between these letters to place the As in. In order to ensure that no two As are adjacent to each other, let us create exactly one slot between any two letters. M __N __ N Additionally, let us add one slot at the beginning and end as well as the As can go there also. __ M __N __ N __ Now, out of these 4 slots, some 3 can be A. That can be selected in 4C3 ways. So, total number of words = 3 ! * 4C3 ways The question is "In how many ways can we rearrange the letters of the word MANANA such that no two A’s are adjacent to each other?" ##### Hence the answer is "3 * 4C3 " Choice C is the correct answer. ###### 🎯 Huge Discount: 3,500 off on Online CAT Course. Till June 1. Register now! ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 40,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in ChennaiRegister Online, get Rs 7000/- off Attend a Demo Class ## 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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