10. Basic Rules of Counting

Try these first

1. 1.

   Using the product rule, if you have 2 flavors of ice cream and 3 types of cones, how many combinations can you create?

   Hint

   Multiply the number of ice cream flavors by the number of cones.

2. 2.

   If you have 4 shirts and can choose to wear either a tie or not, how many options do you have?

   Hint

   Consider each shirt with two choices: with a tie or without.

3. 3.

   What does the Product Rule in counting describe?

   • Adding choices
   • Multiplying sequences of independent choices
   • Finding overlaps

   Hint

   Think about tasks done sequentially.

4. 4.

   True or False: The Pigeonhole Principle states that if you have 10 items placed into 9 containers, at least one container will hold two items.

   • True
   • False

   Hint

   Consider containers and items.

5. 5.

   You have a choice between 5 appetizers and 7 main courses for a party; how many distinct meal combinations can you create? Now include choosing 2 desserts from 4.

   Hint

   Break it into parts and multiply.

6. 6.

   At a contest, 100 participants are split into 90 different teams. Confirm using the pigeonhole principle that at least one team has more than one participant.

   Hint

   Think about the overflow concept in containers.