Question

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

• A. $14$
• B. $15$
• C. $16$
• D. $56$

Answer 1

The correct option is C $16$

Fixing $1$ as the first digit
1 _ _ _
We get $3!$ numbers $=6$ ...(i)
Fixing $2$ as the first digit
2 _ _ _
We get $3!$ numbers $=6$ ...(ii)
Fixing $3$ as the first digit and $1$ as the second digit, we get
3 1 _ _
We get $2!$ numbers $=2$ ...(iii)
Now fixing $3$ as the first digit and $2$ as the second, we get two numbers $3214$ and $3241$.
$\therefore$ The rank of the number $3241$
$=6+6+2+2$
$=16$