Watch the videos to review what you have learned about combinations and see more combination problems involving AND conditions.
Combinations

Combining
 

 

Combination problems can also involve OR conditions . Recall from Lesson 2C that OR conditions involve adding cases that are related directly to the conditions set out in the problem. This is known as direct reasoning . In some problems, you can also use indirect reasoning to solve a combination problem. Read in your text to understand how these reasoning methods are related.

 

Read page 116 Example 4 and pages 124-125 Example 3 in your textbook, Principles of Mathematics 12 .

Complete the Your Turn questions on page 117 (part a) and page 125 to compare direct and indirect reasoning.

Click here to verify your answers .

 

After completing the Your Turn questions, you should have noticed that indirect reasoning is an efficient way to solve given a small group , in other words a small n value . The larger group the more difficult indirect reasoning becomes.

In this unit, you have learned about both permutations and combinations. You must be able to distinguish the type of counting problem before you begin solving. As you watch the following video, pay particular attention to how the type of problem is identified and what solving method is used as a result . Use the flowcharts provided at the beginning of Lessons 2C and 2D to help guide you.

 

Watch the Solving Counting Problems video to review solving permutation and combination problems

As you watch the video, pause at each question and solve on your own; then, check your work by viewing the solution in the video.

The example How many ways can 5 people sit around the table? is a circular permutation and is beyond the scope of this course. You may skip this example when watching the video.

 

Read pages 117 In Summary , page 125 In Summary , and pages 130-131 Frequently Asked Questions in your textbook, Principles of Mathematics 12 .