Question

If a $5$ digit number is created using the digits $1,2,3,3,5$. If all possible numbers are arranged in ascending order, then the number situated at ${51}^{th}$ position is

• A. $52133$
• B. $51323$
• C. $51233$
• D. $51332$

Answer 1

The correct option is D $51332$

Available digits are : $1,2,3,3,5$
Numbers starting with $1\left(1\_\_\_\_\right)$
$=\frac{4!}{2!}=12$
Numbers starting with $2\left(2\_\_\_\_\right)$
$=\frac{4!}{2!}=12$
Numbers starting with $3\left(3\_\_\_\_\right)$
$=4!=24$
Total numbers till now $=12+12+24=48$

Now, numbers starting with $51$ $\left(51\_\_\_\right)$
$=\frac{3!}{2!}=3$
Total numbers $=51$
So,
$51233$ is at ${49}^{th}$ position
$51323$ is at ${50}^{th}$ position
$51332$ is at ${51}^{th}$ position