Plato gave you "the formula"...
go read up:
Introduction to Combinations | | Mathematics and MultimediaMathematics and Multimedia
N=4 sons (1234) to separate into K=3 groups, using K-1=2 dividers (--).
So 123-4- means 3,1,0
So 1-23-4 means 1,2,1
So we have to choose K-1=2 dividers among N+K-1=4+2=6 symbols,
so #ways is (6 over 2), or (4+3-1 over 2), or (N+K-1 over K-1), or (N+K-1 over N)