Question

The sum of the unit digits of all $5$ digit numbers that can be formed using $0,1,3,4$ and $6$ without repetition, is

Answer 1

If we fix any digit except $0$ in the unit place, then the other digits can be arranged in
$3\times 3\times 2\times 1=18$ ways
If unit digit is $0,$ then the sum will be $0$.

Hence the required sum will be $18\times (1+3+4+6)=252$