But the worst kind of questions for binomial series expansion must be those questions asking for the $x^r$ term! If you're not from AJC, you may not even have seen such a question! An example of such question is from the actual A levels examination paper in N94/1/15 (below).
Find, in the simplest form, the coefficient of $x^r$ in the expansion, in ascending powers of $x$, of $\frac{1}{\left ( 1-x \right )^{3}}$.
Many students find this kind of questions difficult. It is quite true, especially for students who were not exposed to the ${n \choose r}$ formula. This video shows how such questions are typically solved. Watch the video on YouTube here.