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Q.
The sum of all the numbers that can be formed with the digits $2,3,4,5$ taken all at a time is
Permutations and Combinations
Solution:
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
$=84\left(1+10+10^{2}+10^{3}\right)=84(1111)=93324$