Question

The sum of all the different four digit numbers that can be formed with the digits $2,3,4,5$ taken all at a time is

• A. $93324$
• B. $93240$
• C. $9324$
• D. none of these

Answer 1

The correct option is A $93324$

Total numbers that can be formed with the digits $2,3,4$ and $5$ taken all at a time is equal to the number of arrangements of
$4$ digits taken all at a time, i.e. ${}^4{P}_4=4!=24$

Now each digit appear on each place in a number $6$ times
Hence sum of digits of each places $=6(2+3+4+5)=84$

Hence required sum is
$=84({10}^0+{10}^1+{10}^2+{10}^3)=93324$