Question

Find the sum of all four digit numbers (without repetition of digits) formed using the digits $1,2,3,4,5$.

Answer 1

Each number will apear at units,tens,thousands,ten thousands place at $4!$ times so when it comes to unit place it should get add $4!$ times .if $5$ comes at unit place it should get add $4!$ times at tens place $10\times 4!$ times,at thousand place ${10}^2\times 4!$ times hence required sum would be

$(4!)(1+2+3+4+5)({10}^0+{10}^1+{10}^2+{10}^3+{10}^4)$

$=3999960$