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Chapter 17 Basic Counting Problems
Exercises Practice Problems
1. Packing a Lunch.
A healthy lunch box contains a sandwich, a piece of fruit and a drink. There are six different types of sandwiches, five kinds of fruit, and three drink flavors. How many different possible lunch boxes are there?
2. Buying Ice Cream.
An ice cream store has five flavors of ice cream: vanilla, chocolate, strawberry, peppermint and bubble gum. When you order a cone, your options are sugar cone, waffle cone and cake cone.
What is the total number of ways to order a single-scoop ice cream cone?
Suppose that we want to order a triple-scoop cone at this ice cream store. Stacking scoops of ice cream is important: a peppermint-vanilla-vanilla cone tastes different from a vanilla-peppermint-vanilla cone. What is the total number of ways to order a triple-scoop ice cream cone?
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The ice cream store also sells quarts of ice cream. When you buy quarts of ice cream, the order that you buy the quarts does not matter: they just go into your shopping bag anyway! How many ways can you buy two quarts of ice cream when ...
Both quarts are the same flavor?
The quarts are different flavors? (Remember that the order of the flavors doesn't matter!)
3. Ultimate Frisbee Tournament.
Four teams are attends Ultimate frisbee tournament.
If each team plays each other team exactly once, how many games are played?
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These four Ultimate teams decide to play a game for fun by mixing up the teams. They put red, blue, yellow and green armbands into a bag, and each player closes her eyes and grabs an armband to determine her team.
How many armbands must be grabbed to ensure that one of the teams has two players?
How many armbands must be grabbed to ensure that one of the teams has five players?