Lesson 5

In Try This 3, you may have noticed that some problems can be solved using a permutation or a combination; however, most problems will not require you to use both. Generally, problems can be solved using only permutations or by using either combinations or permutations.

This table shows how to solve question 3 from Try This 3 using permutations.

5P3 = 60	Determine the number of favourable outcomes—that is the number of different ways 3 of the balls numbered 4, 5, 6, 7, and 8 can be pocketed if order is considered important.
8P3 = 336	Determine the number of total outcomes—that is the total number of ways 3 of the balls numbered 1, 2, 3, 4, 5, 6, 7, and 8 can be pocketed if order is considered important.
	Determine the probability.

This table shows how to solve question 3 from Try This 3 using combinations.

5C3 = 10	Determine the number of favourable outcomes—that is the number of different ways 3 of the balls numbered 4, 5, 6, 7, and 8 can be pocketed if order is not considered important.
8C3 = 56	Determine the number of total outcomes—that is the total number of ways 3 of the balls numbered 1, 2, 3, 4, 5, 6, 7, and 8 can be pocketed if order is not considered important.
	Determine the probability.

If you would like another example of how to solve probability problems using combinations, watch the video titled “Probability Using Combinations.”

Self-Check 2

1. An e-mail contact list contains 21 friends, 18 family members, and 5 co-workers.
   1. Determine the probability that the last 10 people are not family members if the list is alphabetized. Create a diagram or visual to help you represent this problem. Answer
   2. What similarities and differences are there between this question and Try This 3 question 3? Answer