Question

The letters of the work 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is ______.

Answer 1

Arranging letters in alphabetical order A D I K M N N to find rank of MANKIND and making arrangements of a dictionary we get
A ………….$\frac{6!}{2!}$=360
D …………. 360
I …………. 360
K …………. 360
M A D ………….$\frac{4!}{2!}$=12
M A I ………….12
M A K ………… 12
M A N D …………. 3! = 6
M A N I …………. 6
M A N K D …………. 2
M A N K I D …………. 1
M A N K I N D …………. 1
∴ Rank of MANKIND = 1440 + 36 + 12 + 2 + 2
= 1492