no. of non negative integral solutions for x+2y+3z=8

The values of z can be 0, 1 or 2

When z=0
Y can be 0, 1, 2, 3 or 4
When z = 1
Y can be 0, 1, 2
When z = 2,
y can be 0, 1
So total number of solutions = 10