A certain mathematician always carries two boxes of matches with him. Whenever he wants a match, he
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A certain mathematician always carries two boxes of matches with him. Whenever he wants a match, he selects one of the boxes at random. Find the probability that when the mathematician draws an empty box, the other box will contain \(r\) matches \((r=0,1,2, \ldots, n ; n\) is the number of matches initially contained in each box).
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