Question

What is the sum of all of the four-digit positive integers that can be written with the digits 1, 2, 3 and 4 if each digit must be used exactly once in each four-digit positive integer?

Answer 1

Answer with explanation:

Number of four digit numbers using four distinct digit

         =Unit placed can be filled in four ways * Tens place can be filled in Three ways * Hundreds place can be filled in 2 ways * Thousand Place can be filled in a single way

=4*3*2*1

=24 distinct numbers

Sum of all four , four digits numbers using 1,2,3,4

          = (If we keep 4 at unit place +Keeping 3 at unit place +Keeping 2 at unit place+Keeping 1 at unit place)×6+At tens place (2*2+3*2+1*2+4*2+2*2+1*2+1*2+3*2+4*2+2*2+3*2+4*2)+At hundred's place (2*2+3*2+1*2+4*2+2*2+1*2+1*2+3*2+4*2+2*2+3*2+4*2)+At thousand's Place(2*2+3*2+1*2+4*2+2*2+1*2+1*2+3*2+4*2+2*2+3*2+4*2)

=(24+18+12+6)Unit place+(60)Ten's place +(60)Hundred's place+(60)Thousand's Place

=66660