Question

The sum of all the four digit numbers formed with the digits $0,1,2,3$ taken all at a time is

• A. $6(4!)$
• B. $38000$
• C. $38664$
• D. $noneofthese$

Answer 1

The correct option is C $38664$

$\begin{array}{c}Theno.canbewrittenas\\ 3\times 3\times 2\times 1=18\\ because0cannotbefilledatfirst\\ \frac{18}{3}=6\\ sumofno.atIplace=6\\ 6\times \left(1+2+3\right)=36\\ sumofno.atIIplace=6\\ 6\times 0+4\left(1+2+3\right)=24\\ sumofno.atIIIplace=6\\ 6\times 0+4\left(1+2+3\right)=\\ sumofno.atIVplace\\ 6\times 0+4\left(1+2+3\right)=24\\ 36\times 1000=36000\\ 24\times 100=2400\\ 24\times 10=240\\ 24\times 1=24\\ =38664\end{array}$

Hence, this is the answer.