Question

Find the sum of all four digit numbers that can be formed using the digits $1,3,5,7,9$.

Answer 1

A digit can be in a place in $4\times 3\times 2$ ways

So for digit $k$ sum of it's influence in all numbers $=(k\times {10}^3+k\times {10}^2+k\times 10+k)4\times 3\times 2$

$=k\times \left(1111\right)4\times 3\times 2$

So for $1,3,5,7,9$

$=\left(1111\right)\times 4\times 3\times 2(1+3+5+7+9)$

$=666600$