What is the rank of the word "MOTHER" when all possible words are formed using all its letters and arranged as in a dictionary?

Step-by-step solution

Total words =6 i =720 Number of words before starting with 'M' =2 5 i=2 120=240 Number of words starts with M and second letterbeore ^ o ^ =2 x 4 i =48 Number of words with first two letters are MOand third letter before T =3 3 i =18 Number of words with first three letter are MOT and fourth letter before H =2 i =2 Total words till now =240+48+18+2=308 Next words = MOTHER So, Rank of MOTHER =308+1=309