Q. 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
A) 240
B) 261
C) 308
D) 309
Explanation
(d)
The number of words starting from E are =5!=120
The number of words starting from H are =5!=120
The number of words starting from ME are=4!=24
The number of words starting from MH are=4!=24
The number of words starting from MOE are =3!=6
The number of words starting from MOH are =3!=6
The number of words starting from MOR are =3!=6
The number of words starting from MOTE are =2!=2
The number of words starting from MOTHER are =1!=1
Hence, rank of the word MOTHER
$= 2(120) + 2(24) + 3(6) + 2 + 1$
$= 309$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.