Question

If all possible four digit numbers are formed with the digits $3,5,6,9$ without repetition and arranged in the ascending order of magnitude, then the position of the number $6953$

• A. $20$
• B. $16$
• C. $18$
• D. $15$

Answer 1

The correct option is C $18$

First set of numbers will have $3$ as the thousands digit.

With three as the thousand's digits, there will be $3$ options for hundredth place, $2$ options for ten's place and 1 for one's place since repetition is not allowed.

Hence number of $4$-digit numbers starting with $3$ are $3\times 2\times 1=6$

Similarly for numbers starting with $5$.

So till now $12$, $4$-digits numbers have been counted.

Also similarly there are $6$, $4$-digit numbers starting with $6$.

The last number out of them will have $9$ at hundred's place, $5$ at ten's place and $1$ at unit's place.

Hence $6953$ is at 18th position.