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.

 

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