∵x,y,z∈N and
x∈A, i.e., and y∈B, i.e., and z∈C, i.e., 1≤x≤89≤y≤1617≤z≤24
∴ Number of solution for
x+y+z=36 is equal to coefficient of
x36in(x+x2+…+x8).(x9+x10+…+x16)⋅(x17+x18+…+x24)=coefficientofx^9
in(1+x+…+x7)3
= coefficient of
x9 in
(1−x)3(1−x8)3
= coefficient of
x9 in \left(1-3 x^8+3 x^{16}-x^{24}\right)
===(1+3x+2!3.4x2+…)11C9−3.355−946
