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  • If the letters of the word ADORE are arranged in all possible ways and the words are arranged in a dictionary, then find the rank of the word ADORE.  <str

If the letters of the word ADORE are arranged in all possible ways and the words are arranged in a dictionary, then find the rank of the word ADORE.

 

Option: 1

4


Option: 2

16


Option: 3

56


Option: 4

38


Answers (1)

best_answer

Given that the word is ADORE. 

The lexicographic order of the letters of the given word is A, D, E, O, R. The words that begin with A will come first in the lexicographic order.

If the letter A is in the first place of the five-letter word, then the remaining four letters can be arranged in 2! ways. On proceeding like this, 

$$ \operatorname{ADE}(--)=2 !\: ways

\operatorname{ADOE}(-)=1 !\: $$ ways

ADORE $=0$ ! \: ways

Therefore, the rank of the word ADORE is 4.

Posted by

Devendra Khairwa

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