Exercise Set 7.2: Pascal’s Triangle & Combinations Find the number of combinations. 1.
5
C2
2.
7
C5
3.
8
C2
4.
9
C6
5.
10
C3
6.
12
C5
First decide whether you need to use multiplication or addition. Then find the number of possibilities for the given situation. 7. A restaurant gives options of 6 vegetables and 4 meats be ordered on a pizza. Suppose you want exactly 3 vegetables and 2 meats on your pizza. How different pizzas can you order? 8. A restaurant gives options of 6 vegetables and 4 meats be ordered in an omelet. Suppose you want exactly 2 vegetables and 3 meats in your omelet. How different omelets can you order? 9. During the school year, the basketball team is scheduled to play 12 home games. You want to attend at least 9 of the games. How many different combinations of games can you attend? 10. During the school year, the basketball team is scheduled to play 10 home games. You want to attend at least 6 of the games. How many different combinations of games can you attend? 11. You are going to buy a bouquet of flowers. The florist has 18 different types of flowers. You want at most 3 types of flowers. How many different combinations of flowers can you use in your bouquet?
12. You are going to buy a bouquet of flowers. The florist has 18 different types of flowers. You want exactly 3 types of flowers. How many different combinations of flowers can you use in your bouquet? 13. You have enough credit on iTunes to purchase six songs. You have narrowed it down to 7 Dubstep songs and 5 Indie rock songs. You want to make a mix that contains 2 Dubstep and 4 Indie songs. How many different mixes can you make? 14. You only like 6 songs on the latest Arcade Fire album. If you want to purchase at most 4 songs with the credit you have on iTunes, how many different combinations can you buy? 15. William Shakespeare wrote 38 plays. Of the 38 plays, 18 are comedies, 10 are histories, and 10 are tragedies. How many different sets of exactly 4 comedies and 2 tragedies can you read? 16. William Shakespeare wrote 38 plays. Of the 38 plays, 18 are comedies, 10 are histories, and 10 are tragedies. How many different sets of at most 4 plays can you read? 17. A local, organic bakery sells 10 different flavors of regular cupcakes, 5 different flavors of gluten-free cupcakes, and 3 different flavors of vegan cupcakes. How many different combinations can you buy if you want exactly 3 regular cupcakes, 2 gluten-free cupcakes, and 1 vegan cupcake?
