Fundamental Counting Principle

Fundamental Counting Principle, Permutations & Combinations

Poll

In the cafeteria, a lunch combo consists of a sandwich, side and dessert. How many different ways do YOU THINK you can choose a lunch combo?

• $$10$$  

• $$16$$  

• $$12$$  

• $$24$$  

• $$48$$  

Objective(s) & Standard

• Use the Fundamental Counting Principle to determine outcomes

• Count Permutations

• Count Combinations

•  MAFS.912.S-CP.2.9 - Use permutations and combinations to compute probabilities of compound events and solve problems.

Multiple Choice

To create an entry code for a push-button door lock, you need to choose a letter and then, three single-digit numbers. How many different entry codes can you create?

• $$26,000$$

• $$56$$

• $$260$$

• $$1026$$

Calculator Check

Multiple Choice

Evaluate $$4!$$  

• $$12$$  

• $$36$$  

• $$24$$  

• $$10$$  

Multiple Choice

Evaluate $$5!3!$$  

• $$40320$$  

• $$720$$  

• $$336$$  

• $$1680$$  

Multiple Choice

Evaluate $$\frac{12!}{6!}$$  

• $$2$$  

• $$665280$$  

• $$720$$  

• $$12560$$  

Multiple Choice

Evaluate $$\frac{10!}{7!3!}$$  

• $$526$$  

• $$720$$  

• $$120$$  

• $$126$$  

Multiple Choice

Evaluate

• $$720$$

• $$56$$

• $$72$$

• $$152$$

Multiple Choice

Evaluate

• $$420$$

• $$840$$

• $$410$$

• $$152$$

Multiple Choice

Evaluate

• $$336$$

• $$56$$

• $$2$$

• $$720$$

Multiple Choice

Evaluate

• $$3603600$$

• $$56$$

• $$32760$$

• $$720$$

Multiple Choice

Determine if the situation is a permutation or combination, and evaluate.

• Combination
  
  $$720$$

• Permutation

  
  $$720$$
  

• Combination

  
  $$70$$
  

• Permutation

  
  $$70$$
  

• Permutation
  
  $$336$$
  

Multiple Choice

In the cafeteria, a lunch combo consists of a sandwich, side and dessert. How many different ways are there for you to choose a lunch combo?

• $$10$$  

• $$16$$  

• $$12$$  

• $$24$$  

• $$48$$  

Multiple Choice

In the cafeteria, a lunch combo consists of a sandwich, side and dessert. If the combos are pre-packaged, what is the probability of choosing a combo with Potatoes?

• $$33$$  

• $$16$$   

• $$12$$   

• $$24$$  

Multiple Choice

How many ways can two jellybeans be chosen from a bag of 15 unique jellybeans. 

• ₁₅C₂=105
• ₁₅P₂=210
• 15 x 2 = 30
• 100 ways

Multiple Choice

How many ways can 5 books be arranged on a shelf?

• 10
• 120
• 1
• 5

Multiple Choice

At  a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?

• 180
• 23
• 12
• 60

Multiple Choice

A menu has 6 different sandwiches, with 3 choices of potato chips, 3 types of salad and 5 different beverages. How many different lunch combinations consisting of a sandwich, chips, salad, and beverage can be ordered?

• 30
• 17
• 90
• 270

Multiple Choice

Find the theoretical probability of NOT landing on yellow if you spin the spinner.

• 1/8
• 7/8
• 1
• 7

Multiple Choice

Homecoming has 7 candidates for King. How many ways can a King and a First Runner-up be chosen to form the Festival Court?

• 23

• 840

• 42

• 3,628,800

Multiple Choice

Johnny's mother had three children. The first was named April. The second child was named May. What was the third child's name?

• June
• July
• March
• None of these

Multiple Choice

The golf club can send a team of four students to the next golf tournament. If there are 15 students in the club, how many different teams of four can be selected?

• 1365

• 259459200

• 60

• 50625

Multiple Choice

There are 18 students playing Quizizz in math class. How many ways can they win the gold, silver, and bronze places on the podium?

• 54

• 816

• 5832

• 4896

Multiple Choice

What would you use to solve the problem?

How many ways can you line up your eight trophies that you've won over the years on a shelf in your room?

• Permutation

• Combination

• Counting Principle

• Factorial

Multiple Choice

There are 5 apples and you take 3. How many apples do you have?

• 5

• 3

• 2

• 0

Multiple Choice

When Jack bought his new truck, there were 96 different ways his truck could be equipped. He had four choices of engines and two choices of transmissions. If the only other choice was color, how many colors were available?

• 11

• 12

• 13

• 14

Multiple Choice

Melanie is taking four classes this semester: American History, Algebra 2, AP English, and Chemistry. How many ways can these four classes be arranged on her schedule?

• 24

• 153

• 765

• 824

How to find Permutations of
letters in a word

Multiple Choice

How many ways can you arrange the letters in the word FACTOR?

• ₆P₆=720
• ₆C₆=1
• 6 x 5 = 30
• 120 ways

Multiple Choice

How many ways can you arrange the letters in the word CHEESE?

• 720

• 120

• 360

• Cheese is life.

Multiple Choice

How many ways can you arrange the letters in the word MATH?

• 100

• 4

• 24

• 16

Multiple Choice

How many ways can you arrange the letters in the word PROBABILITY?

• 9,979,200

• 39,916,800

• 19,958,400

• Prob/Stats is the best math class ever.