A secretary is sorting 34 distinct files into 2 distinct cabinets. 1. Suppose that file order does not matter within the cabinets. How many ways can you sort the files into the cabinets? Assume the cabinets have infinite capacity. 2. Suppose that file order matters within the cabinets. How many ways can the files be sorted into the cabinets? Assume the cabinets have infinite capacity. 3. Assume that all cabinets have a maximum capacity of 17 files. In other words, each cabinet can hold at most 17 files. How many ways can the files be sorted into the cabinets? Again, assume that file order matters within the cabinets.

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