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A tea-drinking Canadian friend of yours claims to have a very refined palate. She tells you that she can tell if, in preparing a cup of tea, milk is first added to the cup and then hot tea poured into the cup, or the hot tea is first poured into the cup and then the milk is added. To test her claims, you prepare ten cups of tea. Five have the milk added first and the other five the tea first. In a blind taste test, your friend tastes all ten cups and is asked to identify the five that had the milk added first.
How many different ways are there to select five of the ten cups?
If your friend is just guessing, what is the probability that she correctly identifies the five cups with the milk added first? (Enter your probability as a fraction.)
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