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GO Classes 2023 | IIITH Mock Test 1 | Question: 96

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All the rearrangements of the word $\text{“DEMAND"}$ are written without including any word that has two $\text{D’s}$ appearing together. If these are arranged alphabetically, what would be the rank of $\text{“DEMAND"}?$

  1. $36$
  2. $74$
  3. $42$
  4. $86$
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The correct option is  74
Alphabets present in the word DEMAND are D,E,M,A,N,D
Dictionary Order of these letters is A,D,D,E,M,N
Words starting with A:5!2!=60
Words starting with A where two D′s are together =4!=24
∴Words starting with ′A′, without two D′s adjacent to each other =60−24=36

Next we have words starting with ′D′.

Within this, we have words starting with DA (DA _ _ _ _): 4! words =24 words
Then words starting with DE
Within this, words starting with DEA (DEA _ _ _)⇒3!=6 words

Then starting with DED (DED _ _ _)⇒3!=6 words
Then starting with DEM
⇒ First word is DEMADN
⇒ Second word is DEMAND

∴Rank of the word DEMAND=36+24+6+6+2=74
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