1. Lesson 3

1.6. Explore 5

Mathematics 30-1 Module 8

Module 8: Permutations, Combinations, and the Binomial Theorem

 

In Try This 3 the coach must choose a centre and a right wing and a left wing and two defence. By using the fundamental counting principle, you multiply the number of choices for each position to determine the total number of ways to make these choices.

  • centre: 5C1 
  • right wing: 7C1
  • left wing: 6C1 
  • two defense: 10C2

The total number of ways the coach can choose the first line is 5 × 7 × 6 × 45 = 9450 ways.

 

This diagram shows 5 centres, 7 right wingers, 6 left wingers, and 10 defense players. At the bottom of the diagram there is a space for a centre, a right winger, a left winger, and two defense players with 5 choose 1 multiplied by 7 choose 1 multiplied by 6 choose 1 multiplied by 10 choose 2 equals 9450 is written below.

Hemera/Thinkstock

 



textbook

If you want to see another example of a combination question with extra conditions, read through the rest of “Example 1” on pages 530 and 531 of the textbook.

 

 

Self-Check 3
  1. The student activities committee consists of 5 students from Grade 10, 5 students from Grade 11, 8 students from Grade 12, and 2 teachers. How many dance subcommittees can be formed if there must be 2 students from each grade and only 1 teacher? Answer
  2. Complete “Your Turn” on the bottom of page 531 of the textbook. Answer