Problem 11.2. In the store, there are 9 headphones, 13 computer mice, and 5 keyboards. In addition, there are 4 sets of "keyboard and mouse" and 5 sets of "headphones and mouse". In how many ways can you buy three items: headphones, a keyboard, and a mouse? Answer: 646.
Solution. Let's consider the cases of whether any set was purchased.

- Suppose the set "keyboard and mouse" was purchased, then headphones were added to it. This results in exactly $4 \cdot 9=36$ ways to make the purchase.
- Suppose the set "headphones and mouse" was purchased, then a keyboard was added to it. This results in exactly $5 \cdot 5=25$ ways to make the purchase.
- Suppose no set was purchased, then headphones, mouse, and keyboard were purchased separately. This results in exactly $9 \cdot 13 \cdot 5=585$ ways to make the purchase. In total, there are exactly $36+25+585=646$ desired ways.