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"?

- 36
- 74
- 42
- 86

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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"?"**

Choice B is the correct answer.

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