What is the sum of all $4$ digit numbers which can be formed using the digits $1,2,4,5$ exactly once

The correct option is A $79992$

Given that $4$ digit number are to be formed from $(1,2,4,5)$ with no repetition $\xi$ to calculate the sum of all possible numbers.

$\Rightarrow$ Total possible numbers $=4!=24.$

$\Rightarrow$ Since its a $4$ -digit number ,each digit will appear $\frac{24}{4}=6$ times in each of the units, tens, hundred $\xi$ thousands place.

$\therefore$ Sum $=6(1+2+4+5)\times 1+6(1+2+4+5)10+6(1+2+4+5)100+6(1+2+4+5)1000$

$=6\times 12\times \left(1111\right)=79992.$

Hence, the answer is $79992.$