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HMMT November 2018 U5

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Jerry has ten distinguishable coins, each of which currently has heads facing up. He chooses one coin and flips it over, so it now has tails facing up. Then he picks another coin (possibly the same one as before) and flips it over. How many configurations of heads and tails are possible after these two flips?

Dataset text NuminaMath olympiads. Quoted with source.

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46

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