# The case of the missing ingredients

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).
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