Question

The sum of all numbers greater than $1000$ formed by using the digits $1,3,5,7$ such that no digit is being repeated in any number is

• A. $72215$
• B. $83911$
• C. $106656$
• D. $114712$

Answer 1

The correct option is C $106656$

$1,3,5,7\to$ four digits

$\therefore$ number of numbers $=4!=24$

We have to find the sum of these $24$ numbers suppose $7$ is in the unit place,

then the remaining three can be arranged as $3!=6$ ways.

Similarly, other digits can occupy the first place in $6$ ways.

Hence, even due to unit place of all the $24$ digits number $=6(7+5+3+1)$ units $=96$ units.

Again suppose $7$ is in the second place i.e., tens place and it will be so in $6$ numbers.

Similarly, each digit will be in tens place of all the $24$ numbers.
$=6(7+5+3+1)$tens $=96\times 10$ units

Proceeding similarly for hundreds and thousands.
The sum$=96(1+10+100+1000)=96\times 1111=106656$