# The case of the missing ingredients

**Discrete Mathematics**Level 5

Suppose you are in the kitchen and are looking for two misplaced ingredients. You know that they are somewhere inside a bank of \(10\) drawers but have no idea which drawer{s} they are in.

Assuming that each ingredient has an equal chance of being in any of the \(10\) drawers, what is the expected number of drawers you will have to open before finding both of the missing ingredients?

If the expected number of drawers is \(\dfrac{a}{b}\), where \(a\) and \(b\) are positive coprime integers, then enter \(a + b\) as your answer.

Clarifications:

- It is possible that both ingredients are in the same drawer.
- You remember which drawers you've opened, so won't open the same one twice.
- Once you open a drawer with the ingredient(s) inside you will subsequently have found the ingredient(s).