Question

The sum of all the four digits number that can be formed with $0,1,2,3,4$ is:

• A. $66660$
• B. $66480$
• C. $259980$
• D. $65520$

Answer 1

The correct option is C $259980$

The sum of all $4$ digit no: with the given digit allowing $0$ to be the $1^{st}$ digit. These are $5\times 4\times 3\times 2=120$ different no:

The digits are evently dispered so each digit appears $\frac{120}{5}$=$24$ times in the $1000$'s place no:, we get $24\times (0+1+2+3+4)\times 1000$=$240000$.

Suming the hundreds place no's ,we get $24000$, $10$'s place =$2400$ and $1^{st}$ place=$240$.

$\therefore$ By adding =$266640$

=$120\times \frac{1}{5}\times (0+1+2+3+4)\times (1+10+100+1000)$

=$240\times 111$

Now by subtracting the start with zero

$(4\times 3\times 2)\times \frac{1}{4}\times (1+2+3+4)\times (1+10+100)$

=$6660$

Hence, the answer is $259980$