1. Counting Problems Problem 1: You’re considering 10 colleges to attend, and will be taking a trip to visit some of the schools. In how many ways can you choose 2 out of the 10 schools to visit?

2. Counting Problems Problem 2: In a survey you are asked to recommend your 2 favorite high school courses. If you are considering 20 courses that you have taken, in how many ways could you choose 2 out of the 20 to recommend?

3. Counting Problems Problem 3: You have won 3 tickets to a very popular concert. From among your 8 closest friends, in how many ways could you choose 2 of them to invite to the concert?

4. Counting Problems Problem 4: As you probably know, a mother has two X chromosomes and a father has one X and one Y chromosome. If each parent contributes one of these chromosomes to an offspring, what are the possible outcomes for that offspring? (What do you think is the probability of each outcome? Why?)

5. Counting Problems Problem 5: While on vacation you decide to eat three meals at your hotel one day. If you have 4 options for breakfast, 5 options for lunch, and 4 options for dinner, how many total possibilities do you have for the three meals that day?

6. Counting Problems Problem 6: You want to order a one-topping pizza at a certain restaurant. This particular restaurant offers 4 different types of crust, as well as a choice from among 12 toppings. How many different one- topping pizzas could you order?

7. Counting Problems Problem 7: A certain car company believes in offering each of its models in several varieties, with few individual options for the buyer. If a given model is available in 3 trim levels, with a choice of 6 exterior colors, how many unique versions of this model are available?

8. Counting Problems Problem 8: Another car company believes in offering customers as much choice as possible. One of its models is available in 3 trim levels, with choices of 7 exterior colors, 3 interior colors, 4 different audio systems, 4 different tire/wheel combinations, air conditioning or no AC, power windows or no PW, 3 engines, and 2 transmissions. How many versions of this model are available?

9. Counting Problems Problem 9: What would be some benefits of following the practices of the car company in Problem 7? In Problem 8?

10. Counting Problems Problem 10: Trivia—Can you guess which nation’s car companies were pioneers in adopting the approach of Problem 7? Can you see how they might have gained a competitive advantage as a result?