If the letters of the word MOTHER are written in all possible orders and these words are written out as in a dictionary, then the rank of the word MOTHER is

detailed solution

Correct option is D

The number of words starting from E are = 5 ! = 120The number of words starting from H are = 5 != 120The number of words starting from ME are = 4! = 24The number of words starting from MH are = 4! =24The number of words starting from MOE are = 3 ! = 6The number of words starting from MOH are = 3!= 6The number of words starting from MOR are = 3 ! = 6The number of words starting from MOTE are = 2 != 2The number of words starting from MOTHER are = 1!= 1Hence, rank of the word MOTHER=2 (120) + 2 (24) + 3 (6) + 2 + 1= 309