Q:

avoiding writing loops

I have a list 
a={1,2,3,4,5}

I want to calculate absolute differences of each element with all other elements 
 b={{0,1,2,3,4},{1,0,1,2,3},{2,1,0,1,2},{3,2,1,0,1},{4,3,2,1,0}}

and then calculate the total for each subarray
  c={10,7,6,7,10}

I want to write it in one line basically, need help here
 b=[#1-a]&/@a  isn't working.

Do someone has an easy way to write it out, instead of using any module loop? thanks in advance

A:

Total[DistanceMatrix[a]]

...too short to be an acceptable answer (minimum is 30 characters) without some meaningless commentary

A:

Total@Outer[Abs[#1 - #2] &, a, a]

