22.2.4. Derangements

Try these first

1. 1.

   What is a derangement?

   Hint

   Think of how people would swap hats without getting their own back.

2. 2.

   Calculate D_2, the number of derangements for two items.

   Hint

   Consider swapping two items.

3. 3.

   What does D_n represent?

   • The number of permutations
   • The number of derangements
   • The number of combinations

   Hint

   Think about what happens to each object in a derangement.

4. 4.

   True or False: The principle of inclusion-exclusion can only be applied to derangements.

   • True
   • False

   Hint

   Consider the broad applications of inclusion-exclusion.

5. 5.

   If you have 8 objects, derive the number of derangements D_8 using inclusion-exclusion.

   Hint

   Break the series down into manageable parts.

6. 6.

   Explore how derangements could apply to a real-world scenario involving seating arrangements.

   Hint

   Consider the permutations in real social contexts.