MDM 4U1
6.3 Probability Using Counting Techniques
Date:_________
Counting techniques of permutations and combinations can be helpful for calculating theoretical probability of
successive or multiple events.
Example 1: Probability Using Permutations
There are 8 Data Management presentations to be scheduled. If Mrs. Dunphy draws lots to determine the dates
for each presentation, what is the probability that Monica will present on the 1st day and Tamara will present on
the 2nd day. Assume that there is only one presentation per day.
Example 2: Probability Using Combinations
A CHS music committee is to be formed consisting of 5 students randomly selected from the 9 members of the
CHS Xpression and the 15 members of the Gaels Fusion.
a. What is the probability that the committee will be comprised of Xpression members, only.
b. What is the probability that the committee will NOT be comprised of Xpression members only.
Example 3: A drawer contains 7 green hats and 4 blue hats. If 3 hats are drawn, calculate the following
probabilities.
a) all 3 hats are green
MDM 4U1
b) 2 hats are green, 1 is blue
c) at least one hat is green
Homework: 1) Exercises
2) Textbook pg.324 # 1,3,5,6,8,9,11 *answer to #11 
2
21
Exercises:
1. There are 9 people on the basketball team. What is the probability that you and your two best friends get to
stand together in the team picture?
2. The Sluggers baseball team has a starting line-up consisting of 9 players. If the batting order is randomly
assigned, what is the probability that Tim will bat first, followed by Amanda?
3. A three-member athletics council is to be randomly chosen from ten students, five of whom are runners.
Determine the probability that:
a. the committee is comprised of all runners?
b. the committee is comprised of the three eldest runners?
c. the eldest runner is president, the second eldest is secretary, and the third eldest is
treasurer?
Answers to Exercises:
1.
2. 0.0138
3. a)
1
12
b)
1
120
c)
1
720