Honors Discrete Chapter 15.1 – 15.3 Test Review Guide
KEY TERMS
 Sample Space
 Random Experiment
 Multiplication Rule
 Sum Rule
 Permutation
 Combination
 Subset
TYPES of PROBLEMS to solve
1) List outcomes of Sample Space
2) Finding Size of Sample Space
 Repetition or Replacement is allowed
 Order Matters
 Order Does Not Matter
 No Repetition or Replacement
 At Most statements
 At Least statements
IMPORTANT FORMULAS:
PERMUTATION:
n
Pr 
( n)!
( n  r )!
COMBINATION: n C r 
( n)!
r! ( n  r )!
PRACTICE TEST PROBLEMS:
1) Find the sample space and the size of the sample space.
a. 4 flips of a coin.
b. Pick a Card from a standard deck looking at the suit of the card and rolling a die.
2) How many different ways you format a paper? If you have the following options:
Text: Times New Roman, Courier, Arial, Georgia, Verdana
Text Size: 10, 11, 12, 14
Spacing: Single, 1.5, Double
3) How many different meals can you eat? If you have the following options:
Appetizer: 5 options, Salad: 3 options, Soup: 4 options, Entree: 6 options, Dessert: 3 options
a. 5-Course Meal: Appetizer, Salad, Soup, Entree, and Dessert
b. 4-Course Meal: Appetizer, Salad or Soup, Entree, and Dessert
c. Appetizer, Salad, and Soup.
d. Entree and Dessert only.
4) Tests and Answer Keys:
a. Find the total number of answer keys for a 15 question, multiple-choice test (A, B, C, D).
b. Find the total number of answer keys for a 15 question, true-false test (T or F).
5) 12 students enter an election with the top 5 vote getters being awarded the class positions
of President, Vice President, Speaker of the House, Secretary, and Treasurer. How many
ways can students be elected to positions?
6) 100 students enter a raffle with 5 prizes.
a. How many ways could students win the 5 prizes if the prizes were identical iPods?
b. How many ways could students win the 5 prizes if the prizes were 5 different gift
certificates?
7) Your college email account asks you to make a new password using numbers and letters.
The password must (1) be 6 characters long, (2) begin with a letter, (3) end in a number, and
(4) it is case sensitive.
a. How many passwords are possible if there are no restrictions?
b. How many passwords last digit is a multiple of 3?
c. How many passwords do not contain your first and last initials?
8) Facebook account now asks you to make a new password using numbers and letters. The
password must (1) be 8 characters long, and (2) it is not case sensitive.
a. How many passwords are possible if there are no restrictions?
b. How many passwords are only numbers?
c. How many passwords are only letters?
d. How many passwords do not contain a repeated character?
e. How many passwords are only numbers without repeated characters?
f. How many passwords are only letters without repeated characters?
9) How many seven-digit numbers (between 1,000,000 and 9,999,999)
a. are odd?
d. First Digit is Even and Last Digit is Odd.
b. No repeated digits?
e. The 2nd digit is a 6 and the 4th is 7.
c. End in 9?
f. All the digits are even?
10) How many four-digit numbers (0 to 9,999)
a. are even?
d. Exactly one digit is a 7.
b. divisible by 5?
e. Begin with an even digit and end with a
prime digit?
c. No repeated digits?
f. Has only even digits, which cannot be
repeated?
11) 8 males and 6 females line up to enter the cafeteria.
a. In how many ways can they line up?
b. In how many ways can they line up if the first person must be a female?
c. In how many ways can they line up if the 1st person must be a male and the 2nd person a
female?
d. In how many ways can they line up if the last person must be a male?
e. In how many ways can they line up if all the women must be ahead of the men?