Question

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

• A. 66666
• B. 84844
• C. 93324
• D. None of these

Answer 1

Answer: (C)

The total number of numbers that can be formed with the digits $2,3,4,5$ taken all at a time $={}^4{P}_4=4!=24$.
Consider the digit in the unit's place in all these numbers.
Each of the digits $2,3,4,5$ occurs in $3!=6$ times in the unit's place
$\therefore$ total for the digits in the unit's place
$=(2+3+4+5)6=84$
Since each of the digits $2,3,4,5$ occurs $6$ times in any one of the remaining places
$\therefore$ the required total
$=84\left(1+10+10^2+10^3\right)=84(1111)=93324$