# Derek's random integers

For positive integers $$A$$ and $$B$$, $$1 \leq A \leq B \leq 100$$, suppose that $$A$$ distinct integers are randomly chosen among the first $$B$$ positive integers. Let $$C$$ be the smallest integer among the $$A$$ integers chosen. How many pairs $$( A,B)$$ are there such that the expected value of $$C$$ is greater than or equal to $$10$$?

This problem is posed by Derek K.

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