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'.

There are 6 letters, each differentBefore MOTHER, words from E , H will comeWords from E = 5! (there are 5 letters to arrange)Words from H = 5!( there are 5 letters to arrange)Now words starting by M will come. First ME will have = 4! (as 4 letters will be arranged)Then MH = 4!Now words with MOFirst words starting with MOE... =3!And words starting with MOH... =3!the words starting with MOR... =3!Now, words starting from MOT will comewords starting with MOTE.. = 2!then after words starting from MOTH will come and first word will MOTHERso, total no. of words before MOTHER = 5! + 5! + 2* 4! + 3 * 3! = 120 +120 + 48 + 18 = 306 so, rank of MOTHER = 307