I was asked about a simple question that is: "What is the coefficient of $x^{18}$ in $(1+x^5+x^7)^{20}$? Generally, we know that; $$(x+y+z)^n= \sum\_{n\_{1}+n\_{2}+n\_{3}=n}\left(\frac{n!}{n\_{1}!n\_{2}!n\_{3}!}\right)x^{n\_{1}} y^{n\_{2}}z^{n\_{3}} $$
So, this question could be answered easily based on above formula. May I ask, if we can find another way for solving such this problem or not. Thanks for sharing the thoughts.