Question 350590
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