The Grinch sneaks into a room with 9 Christmas presents to 9 different people. He proceeds to switch the name-labels on the presents. How many ways could he do this if: a. No present is allowed to end up with its original label? Explain what each term in your answer represents. 362880 b. Exactly 4 presents keep their original labels? Explain. 126 c. Exactly 8 presents keep their original labels? Explain. 9

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