Question

All the numbers that can be formed using the digits $1,2,3,4$ are arranged in the increasing order in magnitude, The rank of the number $3241$ is

Answer 1

$[1,2,3,4]$

Find rank of $3241$

Assumption $1----\Rightarrow 3!$ ways

$2---\Rightarrow 3!$ ways

$31--\Rightarrow 2!$ ways

$3214\Rightarrow 1!$ ways

Required $3241\Rightarrow 1!$ ways

$\Rightarrow$ Rank $=3!+3!+2!+1!+1!$

$\Rightarrow 6+6+2+1+1$

$3241\Rightarrow 16$