Question

How many $4$ digits number less than $7000$ can be formed using the digits $0,5,7,1,2,6,8$?

• A. $480$
• B. $960$
• C. $240$
• D. $120$

Answer 1

The correct option is A $480$

We have to find number of four digit numbers less than $7000$ formed by using the digits $0,5,7,1,2,6,8$ which is similar to filling $4$ vacant place with $7$ different things and by applying some constraints.


First constraint is that all numbers should be less than $7000$ which means digits $7$ and $8$ cannot be filled in thousandth place.

Second constraint is $0$ cannot be filled in thousandth place because it will form $3$ digit number.

So, there are $4$ possibilities of filling thousandth place.

For remaining places no constraints are there.

So, hundredth, ten's and one's place can be filled in $6,5,4$ number of ways respectively.

Total number of $4$ digit numbers formed less than $7000$ are $4\times 6\times 5\times 4=480$