# SOLUTION: if the letters of the word 'MOTHER'are written in all possible order and these words are written out as in dictionary ,find the rank of the word 'MOTHER'.

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 Question 350590: if the letters of the word 'MOTHER'are written in all possible order and these words are written out as in dictionary ,find the rank of the word 'MOTHER'. Answer by sudhanshu_kmr(1152)   (Show Source): You can put this solution on YOUR website!There are 6 letters and all are different. In dictionary, words starting from E, H will come before word MOTHER. so, total no. of words starting from E = 5!= 120 (we have to arrange 5 letters on five places) similarly, no. of words starting from H = 5! = 120 now, first word starting with letter M will come.. similarly, no. of words starting with ME.... = 4! no. of words starting with MH.... = 4! now, words starting from MO will come no. of words starting with MOE... =3! no. of words starting with MOH... =3! no. of words starting with MOR... =3! now, words starting from MOT will come no. of words starting with MOTE.. = 2! then after words starting from MOTH will come and first word will MOTHER so, total no. of words before MOTHER = 5! + 5! + 2* 4! + 3 * 3! = 120 +120 + 48 + 18 = 306 so, rank of MOTHER in dictionary = 307