We want to find the number of all possible combinations from a task. This can be viewed as a multi-stage process (see tree diagram below). The solution is simply the product of the number of options at each stage. **Example:** You have 3 shirts, 2 jeans and 3 ties, where $r_i$ denotes the number of available options in stage $i$. How many outfit combinations are there? $ \begin{rcases} r_1=3 \\r_2=2 \\r_3=3 \end{rcases} \implies \prod_{i=1}^n r_i $ ![[basic-counting-principal.png|center|400]]