Exercise 10.

The Grinch sneaks into a room with 6 Christmas presents to 6 different people. He proceeds to switch the name-labels on the presents. How many ways could he do this if:

1. No present is allowed to end up with its original label? Explain what each term in your answer represents.

2. Exactly 2 presents keep their original labels? Explain.

3. Exactly 5 presents keep their original labels? Explain.