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I have two hats. In one hat are balls numbered 1 through 15. In the other hat are balls numbered 16 through 25. I first choose a hat, then from that hat, I choose 2 balls, without replacing the balls between selections. How many different ordered selections of 2 balls are possible? (By "ordered selections," we mean that "Ball 1 then ball 2 " is considered different from "Ball 2 then ball 1.")

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