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)

$93324$

The total number of the 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 $=(2+3+4+5)\times 6=84$

Since each of the digits $2,3,4,5$ occurs $6$ times in any one of the remaining places, therefore, the required total

$=84(1+10+{10}^2+{10}^3)=84\left(1111\right)=93324.$