# CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

###### CAT Questions | Permutation Probability | Alphabetical Order

The question is from Permutation and Combination. This question is about Alphabetical Order. We need to find out the rank of a particular six letter word. 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 13: All the rearrangements of the word "DEMAND" are written without including any word that has two D's appearing together. If these are arranged alphabetically, what would be the rank of "DEMAND"?

1. 36
2. 74
3. 42
4. 86

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### Explanatory Answer

##### Method of solving this CAT Question from Permutation and Combination: One unit number theory and one unit Combinatorics makes a potent combination for fabulous questions!

Number of rearrangements of word DEMAND = $$frac{6!}{2!}\\$ = 360 Number of rearrangements of word DEMAND where 2 D’s appear together = 5! = 120 Number of rearrangements of word DEMAND where 2D’s do not appear together = 360 – 120 = 240 Words starting with ‘A’; without two D’s adjacent to each other Words starting with A: $\frac{5!}{2!}\\$ = 60 Words starting with A where 2 D’s are together = 4! = 24 Words starting with ‘A’, without two D’s adjacent to each other = 36 Next we have words starting with D. Within this, we have words starting with DA: 4! words = 24 words Then words starting with DE Within this, words starting with DEA => 3! = 6 words Then starting with DED – 3! = 6 words Then starting with DEM => First word is DEMADN => Second is DEMAND Rank of DEMAND = 36 + 24 + 6 + 6 + 2 = 74 The question is "If these are arranged alphabetically, what would be the rank of "DEMAND"?" ##### Hence the answer is "74" Choice B is the correct answer. ###### Online CAT CoachingTry it free! Register in 2 easy steps and start learning in 30 seconds! ###### Already have an Account? ###### CAT Coaching in Chennai Next Weekend Batch Starts Sat, Mar 23rd, 2019 ###### Best CAT Coaching in Chennai Sign up for a Free Demo of our CAT Coaching in Chennai ## 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, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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