what is the number of solution of x+y+z=17 in non- negative integers is:

the book answer is: (17+3-1 C 17)=19C17=171

but i dont unserstand why 17 and not 18???

because there are 18 digits from 0 to 10

so the answer not sepose to be (18+3-1 C 17) = 20C17

???