1. Lesson 4

1.11. Explore 7

Mathematics 30-2 Module 3

Module 3: Permutations, Combinations, and the Fundamental Counting Principle

 

In Piano Chords, you saw that cases were required because you could use 3 or 4 fingers or 2, 3, or 4 fingers. The number of combinations for each case was then added to determine the number of combinations.


textbook

To see another example of solving a combination problem by considering cases, read “Example 4” on page 116 of your textbook. As you read, think about when it would be more efficient to use indirect reasoning rather than direct reasoning.

 

tip
Direct reasoning is working directly with the information provided to find the answer. Indirect reasoning is systematically eliminating possibilities to arrive at the answer.

 



Self-Check 4
  1. Complete “Your Turn” on the top of page 117. In your answer, note when you would use indirect reasoning over direct reasoning. Answer
  2. There are 8 boys and 5 girls in the debate club. A team of 5 students must be chosen for a competition. There must be at least 2 boys selected.
    1. Show how you would calculate this answer using direct reasoning. Answer
    2. Show how you would calculate this answer using indirect reasoning. Answer
    3. Which method involves fewer calculations? Answer