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Use the following information to answer the coming two questions. Twenty-two indistinguishable items are to be...

Use the following information to answer the coming two questions. Twenty-two indistinguishable items are to be placed into five boxes numbered from 1 to 5.

– How many ways are there so that all balls go to the odd-numbered boxes?

– Given that box 1 receives exactly one ball, what is the probability that the boxes are filled in such a way that 11 balls fall in the even-numbered boxes and 11 balls fall in the odd-numbered boxes, assuming all arrangements are equally probable?

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