Permutations and Combinations

[Artermis]

If anyone is able to help me with this question regarding introductory Data Management, I would be grateful.

Find the sum of all the five digit numbers that can be formed using the digits 1,2,3,4, and 5 without repeating any digit.

Thank you!

Artermis

 

[robert Ihnot]

Well, if you had one digit,it would be 1. If you had two, it would be two. If you had three digits, 1,2,3; well then we have 123,132,231,213, 312,321 = 6, and so on...

 

[Galileo]

Any permutation of the 5 digits will give a different number, so there are 5!=120 numbers in total. If you list them vertically (and mentally ofcourse) you can see that adding them is relatively simple by adding the ones digits, tens digits, etc seperately. There are 4!=24 numbers ending in 1, 24 ending in 2 etc. So the sum of the ones digits is 24(1)+24(2)+..+24(5)=24(1+2+3+4+5)=360
Likewise, the contribution of the tens digits is: 10 x 24(1+2+3+4+5)=3600
etc.