number of non-negative integral solutions of

a+b+c+d<=15 ?

816 is the answer 

15+4-1c4-1

18c3 u will get the answer 816

let me start with a example,

If you have |||| (4 identical bars) and you have to divide between 3 people how would you do?

The places are ||-|-| So, two things are helping to separate identical things between 3 people, how many combinations possible here?

It is just like the arrangement of 4 bars and 2 dashes (6C2) or simply 4+3-1C3-1

So like this it is here,

15+4-1C4-1 = 18C3