How many solutions in non-negative integers are there to the equation w + x + y + z = 9?

How many solutions in positive integers?

Think i figured out the first part which i got to be

But how do i calculate the second part? So far im at 220 - (number of solutions with three 0's in it) - (number of solutions with two 0's in it) - (number of solutions with one 0 in it) = 220 - (4) - (6 x 8) - ?

Is there a formula or is it just a counting exercise for the second part?