22.1.6. Applications of the Alternate Form

Try these first

1. 1.

   What is the formula for finding the size of the union of two sets using inclusion-exclusion?

   Hint

   Think about over-counting common elements.

2. 2.

   Define what a derivation means in mathematics.

   Hint

   Consider the example of hats being swapped among people.

3. 3.

   What principle is used to handle overlapping sets when counting their union?

   • Inclusion-Exclusion
   • Fundamental Counting
   • Permutations

   Hint

   Recall the correction method for common elements.

4. 4.

   Is a derangement possible for 1 object?

   • True
   • False

   Hint

   Consider the nature of placement with just one option.

5. 5.

   Calculate the number of derangements for a set of 5 elements.

   Hint

   Use the formula derived from inclusion-exclusion.

6. 6.

   Determine the number of distinct ways to group 7 people into 3 distinct teams, ensuring each team has at least one member.

   Hint

   Think about how to assign members while avoiding empty groups.