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1) A woman has three skirts, five shirts, and four hats. How many different outfits can she wear if she picks one skirt, one shirt, and one hat for her outfit?
2) How many different five-digit ZIP codes are possible if the digits can be repeated?
3) How many different five-digit ZIP codes are possible if the digits cannot be repeated?
4) In how many ways can a baseball manager arrange a batting order of nine players?
5) A store manager wishes to display six different brands of laundry soap by lining them up in a row on a shelf. In how many ways can this be done?
6) There are 8 different statistics books, 6 different geometry books, and 3 different trigonometry books being considered for next year. In how many ways can a textbook committee select one of each book?
7) At a film festival, there are eight different films that will be shown. In how many different orders can these films be shown?
8) The call letters of a radio station must have four letters. The first letter must be a K or a W. How many different call letter combinations are possible if letters may not be repeated?
9) The call letters of a radio station must have four letters. The first letter must be a K or a W. How many different call letter combinations are possible if letters may be repeated?
10) How many different four-digit ID tags can be made if repeats are allowed?
11) How many different four-digit ID tags can be made if it must start with a 7 and no repeats are allowed?
12) In how many different ways can the Harry Potter series of books (7 books total) be arranged in a row on a shelf?
[Figure5]
13) In how many different ways can a manager select a pitcher - catcher combination if the manager has 5 pitchers and 2 catchers to choose from?
14) A coin is tossed 8 times. How many different outcomes are there for this series of 8 flips?
15) Six different colored tiles are available to make a pattern in a row of floor tile. How many possible different 4-color patterns are possible if no colors may be repeated?
16) Six different colors of tile are available to make a pattern in a row of floor tile. Many tiles of each color are available. How many 4-color patterns can be made if colors may be repeated?
17) Four cards are dealt from a standard deck of 52 cards. In how many different orders of suit could the cards be dealt? For example, one order is Club, Heart, Club, Diamond.
18) A pizza restaurant offers 6 different toppings for their pizzas. How many different pizzas are possible?
[Figure6]
19) Use a tree diagram to find all possible outcomes for the result of a series of coin flips if the coin is flipped two times. Write a list of the possible results when complete.
20) The Super-Cool Ice Cream Shoppe sells sundaes, cones, or ice cream bars. You will pick either butterscotch or chocolate and you may choose to have it with nuts or without nuts.
a) Draw a tree diagram to illustrate the different types of ice cream treats that you could order.
b) How could you find the number of outcomes using the Fundamental Counting Principle?
c) How many different outcomes are possible?
21) A quiz has four true/false questions on it. Use a tree diagram to show all the different possible answer keys.
22) A box contains a $1 bill, a $5 bill, and a $10 bill. Two bills are selected one after the other without replacing the first bill. Draw a tree diagram to show all possible amounts of money that may be drawn.
23) The Eagles and Hawks play each other in a hockey tournament. The first team to win two games is the champion. Use a tree diagram to show all different possible outcomes for the tournament.
Review Exercises
24) Consider a situation in which a baseball manager must decide which one of 4 players will pitch (P1, P2, P3, or P4) and which one of 2 players will catch (C1 or C2).
a) What is the sample space for this situation?
b) How many outcomes are possible?
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Image Attributions
- [1]^ License: CC BY-NC 3.0
- [2]^ License: CC BY-NC 3.0
- [3]^ License: CC BY-NC 3.0
- [4]^ License: CC BY-NC 3.0
- [5]^ License: CC BY-NC 3.0
- [6]^ License: CC BY-NC 3.0
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