Order Matters: Mastering Permutations, Combinations, and Probability

Algebra 2 Grades High School 20:54 Video
Print Lesson Plan Watch Video

Lesson Description

Explore the fundamentals of permutations, combinations, factorials, and probability with real-world examples, enhancing problem-solving skills in Algebra 2.

Video Resource

Permutations Combinations Factorials & Probability

Mario's Math Tutoring

Duration: 20:54
Watch on YouTube

Key Concepts

  • Permutations (nPr): Order matters
  • Combinations (nCr): Order does not matter
  • Factorials: The product of all positive integers less than or equal to a given number
  • Probability: The measure of the likelihood that an event will occur

Learning Objectives

  • Students will be able to differentiate between permutations and combinations.
  • Students will be able to apply the formulas for permutations and combinations to solve problems.
  • Students will be able to calculate probabilities using permutations, combinations, and factorials.

Educator Instructions

  • Introduction (5 mins)
    Begin by introducing the concepts of permutations, combinations, factorials, and probability. Briefly explain how these concepts are used in real-world scenarios.
  • Video Viewing (20 mins)
    Play the 'Permutations Combinations Factorials & Probability' video by Mario's Math Tutoring. Encourage students to take notes on the formulas and examples provided. Pause the video at key points (e.g., after explaining each formula) to allow students to process the information.
  • Concept Clarification and Formula Review (15 mins)
    Review the formulas for permutations (nPr) and combinations (nCr). Work through examples from the video, clarifying any points of confusion. Emphasize the difference between permutations (order matters) and combinations (order does not matter). Explain the factorial formula and it's use cases.
  • Problem-Solving Practice (25 mins)
    Present additional word problems that require the use of permutations, combinations, and factorials. Have students work individually or in pairs to solve the problems. Provide guidance and feedback as needed. Example problems: 1. How many different 4-digit PINs can be created if digits cannot be repeated? (Permutation) 2. A committee of 5 people is to be chosen from 10 people. How many different committees are possible? (Combination) 3. What is the probability of drawing 2 aces from a standard deck of cards without replacement? (Probability using combinations)
  • Wrap-up and Q&A (5 mins)
    Summarize the key concepts covered in the lesson. Answer any remaining questions from students. Preview upcoming topics related to probability and statistics.

Interactive Exercises

  • Card Drawing Simulation
    Simulate drawing cards from a deck (either physically or using a program) to demonstrate probability calculations. For example, calculate the probability of drawing a specific card or a combination of cards.

Discussion Questions

  • In what real-world scenarios might you use permutations or combinations?
  • Explain the difference between a permutation and a combination in your own words.
  • How does the factorial function relate to permutations and combinations?

Skills Developed

  • Critical thinking
  • Problem-solving
  • Mathematical reasoning

Multiple Choice Questions

Question 1:

Which of the following scenarios involves a permutation?

Correct Answer: Arranging 5 people in a line for a photo.

Question 2:

What is the value of 5! (5 factorial)?

Correct Answer: 120

Question 3:

In a combination, does the order of selection matter?

Correct Answer: No, order never matters.

Question 4:

How many ways can you choose a committee of 3 people from a group of 7?

Correct Answer: 35

Question 5:

If there are 8 runners in a race, how many different ways can they finish first, second, and third?

Correct Answer: 336

Question 6:

What does nPr represent?

Correct Answer: The number of permutations of n objects taken r at a time.

Question 7:

What does nCr represent?

Correct Answer: The number of combinations of n objects taken r at a time.

Question 8:

If a coin is flipped 3 times, what is the probability of getting exactly 2 heads?

Correct Answer: 3/8

Question 9:

What is the formula for nPr?

Correct Answer: n! / (n-r)!

Question 10:

What is the formula for nCr?

Correct Answer: n! / (r! * (n-r)!)

Fill in the Blank Questions

Question 1:

A(n) ________ is an arrangement of objects in a specific order.

Correct Answer: permutation

Question 2:

The product of all positive integers from 1 to n is called a ________.

Correct Answer: factorial

Question 3:

In a(n) ________, the order of the selected items does not matter.

Correct Answer: combination

Question 4:

The formula for calculating permutations of n objects taken r at a time is ________.

Correct Answer: n! / (n-r)!

Question 5:

The formula for calculating combinations of n objects taken r at a time is ________.

Correct Answer: n! / (r! * (n-r)!)

Question 6:

_______ factorial is equal to 1.

Correct Answer: Zero

Question 7:

Probability is defined as the number of successful outcomes divided by the ________ possible outcomes.

Correct Answer: total

Question 8:

When there are multiple identical letters in a word, you must divide out the _________ to find the number of distinguishable permutations.

Correct Answer: multiplicities

Question 9:

The ___________ counting principle can be used to determine the number of outcomes possible.

Correct Answer: multiplication

Question 10:

When a problem uses the phrase 'at least one,' a good strategy is to take the total minus ________.

Correct Answer: none

Educational Standards

A2.D.3:Use probability to evaluate outcomes of decisions. A2.D.3.2:Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans