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An inspector is visiting a manufacturing facility to identify potential safety violations, and must decide the order in which they will inspect thirteen stations at the facility. Seven are production stations, four are packaging stations, and two are shipping stations. For inspection purposes, stations of the same type are considered indistinguishable.
(1) In how many orders can the stations be visited?
(2) Suppose that the inspecting a production station requires special tools that must be recharged after being used, so the inspector cannot visit two production stations in a row. Re-solve Part (a) for this scenario.
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