Mathematics - Permutation & Combination Question with Solution | TestHub

$\mathrm{M}$

$\mathrm{A}$

$\mathrm{N}$

$\mathrm{K}$

$\mathrm{I}$

$\mathrm{N}$

$\mathrm{D}$

Arranging the letters alphabetically, we get

ADIKMNN

When the word starts with any of the letters A/D/I/K, the number of possibilities$=\frac{6!}{2!}\times 4=1440$

Now when the word starts with MA, then the number of possibilities$=\frac{4!}{2!}\times 3=36$

Now when the word starts with MAN, then the number of possibilities$=3!\times 2=12$

Now when the word starts with MANK, then the number of possibilities$=4$

Hence, rank of the work MANKIND is $1492$