Question

All the numbers that can be formed using the digits, $\{1,2,3,4\}$, are arranged in the increasing order of magnitude. The rank of the number $3241$ is (repetition not allowed)

• A. $58$
• B. $15$
• C. $50$
• D. $16$

Answer 1

The correct option is D $16$

Numbers starting with: Number count

$1^{st}$ digit$=1:3!$

$1^{st}$ digit $=2:3!$

$1^{st}$ digit $=3$ and $2^{nd}$ digit $=1:2!$

$1^{st}$ digit $=3$ and $2^{nd}$ digit $=2$ and 3rd digit $=1:1!$

Next number is $3241:1$

Total Numbers formed will be:

$3!+3!+2!+1!+1!=6+6+2+1+1=16$