The generating function method is to use

• term with different power to represent different object: i.e. power is the value.
• coefficients of these terms to represent the count: i.e. coefficient is the count

While the generating function method is easy to follow and use, the calculation may be tedious. Sometimes the coefficient can be manually obtained by using various polynomial related techniques. However, in many caes, such manual computation may be challenging. In such cases, you are allowed to use tools such as wolframalpha to help expand the generating function, or simply give the generating function and describe which term's coefficient is the desired answer.