If the letters of the word ' MOTHER ' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word ' MOTHER ' is.....

Step-by-step solution

' MOTHER ' Rearrange in alphabetic order EHMORT Number of words start with E = 5 ! Number of words start with H = 5 ! Number of words start with ME = 4 ! Number of words start with MH = 4 ! Number of words start with MOE = 3 ! Number of words start with MOH = 3 ! Number of words start with MOR = 3 ! Number of words start with MOTE = 2 ! Number of word MOTHER = 1 2 × 5 ! + 2 × 4 ! + 3 × 3 ! + 2 ! + 1 = 240 + 48 + 18 + 2 + 1 = 309