Q28 of 31 Page 7

If all letters of word ‘MOTHER’ are written in all possible orders and the word so formed are arranged in a dictionary order, then find the rank of word ‘MOTHER’?

Word is MOTHER.


In a dictionary we arrange letters in alphabetical order. The words will be in sequence E,H,M,O,R and T.


Number of words starting with E = 5! = 120


Number of words starting with H = 5! = 120


Number of words starting with M = 5! = 120


As one of them is MOTHER.


Number of words starting with ME = 4! = 24


Number of words starting with MO = 4! = 24


As one of them is MOTHER.


Number of words starting with MOE = 3! = 6


Number of words starting with MOH = 3! = 6


Number of words starting with MOR = 3! = 6


Number of words starting with MOT = 3! = 6


As one of them is MOTHER.


The first word starting with MOT is MOTEHR.


The second word is MOTERH.


The third word is MOTHER>


∴ Rank of MOTHER = 2(12) + 2(24) + 3(6) +3


= 309


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