I think this is a high-quality question and I don't agree with the explanation. So as per solution you are taking the case where n=k but what about when n<k lets say n=5 and k=6,set A={1,2,3,4,5,6}, now when n=5 probability will be 2 /5! and not 1/5! , because the n=5 can be {1,2,3,4,5} and {2,3,4,5,6}
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