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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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