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. $38646$

Answer 1

Answer: (C)

A four digit number to be formed with digits $0,1,2,3$ taken all at a time. If $1$ will be in units place, we have four such numbers and so $2$ and $3$ will come in unit place four times.
Hence sum in units place $=4(1+2+3)=24$.
So will the sum be in tens and hundreds place. But in thousands place $1$ will come $6$ times and so the other non-zero digits. Hence sum in thousand's place will be
$=6(1+2+3)=6\times 6=36$.
Hence, the required sum is
$36\times 1000+24\times 100+24\times 10+24=38664$.