Some problems involve both permutation and combination. A typical scenario is when all the objects can be divided into several sub-groups. Objects within each group are not distinguishable (hence order does not matter - combination), but different groups are distinguishable (hence order does matter - permutation). These two basic elements can be organized in different ways: permutation of permutation, permuation of combination, combination of combination, and combination of permutation. Regardlessly, the basic techniques to solve them are the same. A generic pattern will be discussed in the lesson Balls in Boxes.

One key point to be carefully determined and considered is whether objects are distinguishable or interexchangeable. 

Note that this lesson has also provided a counting explaination of the multinomial theorem. The expression $$\frac{n!}{r_1!r_2!\cdots r_k!}$$ where $r_1+r_2+\cdots+r_k=n$ is the coefficient of the term $x_1^{r_1}x_2^{r_2}\cdots x_k^{r_k}$ when we expand the polynomial $(x_1+x_2+\cdots+x_k)^n$. If you have already known the binomial theorm, you may notice that the binomial theorm is a special case when $k=2$.