...and where no digit is to be repeated in any 4-digit number.
Yes, I am aware of similar questions on this site, but none of the answers gave me insight as to how this works.
I would like an answer in ridiculously simple terms, like explaining it to a 5 year old.
Total numbers formed using those 5 digits is 5P4. i.e. 120 numbers.
Since all digits will equally occupy the unit's place, therefore 1 will occur 24 times in unit's place. Similarly 2 will occur 24 times in unit's place. So on and so forth. Therefore sum of all digits in unit's place will be equal to 24 x (1+2+3+4+5)=24 x 15.
Similarly sum of all digits in ten's place will be equal to 24 x 150.
Therefore total sum of all numbers =24 x (15+150+1500+15000)=399960 .
Why is there the sum (1 + 2 + 3 + 4 + 5)? Am I misreading the question? Does "no digit is to be repeated in any 4-digit number" mean that there shouldn't be a number like 4432, or does it mean that a number should not be repeated in the same "unit slot"?