Q. 24

If the letters of the word ‘MOTHER’ are written in all possible orders and these words are written out as in a dictionary, find the rank of the word ‘MOTHER’.

Answer :

Given the word MOTHER.

Arranging the permutations of the letters of the word MOTHER in a dictionary:


To find: Rank of word MOTHER in dictionary.


First comes, words starting from letter E = 5! (5 letters no repetation) = 120


words starting from letter H = 5! (5 letters no repetation) = 120


words starting from ME = 4! (4 letters no repetation) = 24


words starting from MH = 4! (4 letters no repetation) = 24


words starting from MOE = 3! (3 letters no repetation) = 6


words starting from MOH = 3! (3 letters no repetation) = 6


words starting from MOR = 3! (3 letters no repetation) = 6


words starting from MOTE = 2! (2 letters no repetation) = 2


words starting from MOTH:


MOTHER = 1


Rank of the word MOTHER = 120 + 120 + 24 + 24 + 6 + 6 + 6 + 2 + 1


= 309


Hence the rank of the word MOTHER in arranging the letters of MOTHER in a dictionary among its permutations is 309.


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