# Questionbank: Permutation and Probability

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## Alphabetical Order

Q.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

Choice B. 74

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## Detailed Solution

Number of rearrangements of word DEMAND = ${6! \over 2!}$ = 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: "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

Correct Answer : 74

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