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  4. The sum of all 4 - digit numbers that can be formed using the digits 2,3,4,5,6 without repetition, is

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Q. The sum of all $4$ - digit numbers that can be formed using the digits $2,3,4,5,6$ without repetition, is

AP EAMCETAP EAMCET 2016

Solution:

We have, digits $2,3,4,5,6$
Sum of all $4$-digit numbers formed by the using $2,3,4, 5,6$ without repetition
$={ }^{4} P_{3}(2+3+4+5+6)\left(10^{3}+10^{2}+10^{1}+10^{0}\right)$
$=24(20)(1000+100+10+1)$
$=(480)(1111)=533280$