Math 30-2
Permutations & Combinations: Lesson #3
Permutations
Objective: By the end of this lesson, you should be able to:
- determine the number of permutations of n objects taken r at a time
- solve a problem involving permutations where all the items are different
Recall: A permutation is
e.g. 1) A high school is holding elections for its Students Union.
Official Ballot
Candidates
Adam
Brittany
Chloe
Dan
Ella
Please choose one candidate for each position. You
may not vote for the same person more than once.
President:
_________________
Vice-President:
_________________
Treasurer:
_________________
a) In how many different ways can this ballot be filled out?
b) How could you write this in factorial notation?
The number of permutations of r objects out of a total of n distinct objects is:
Note: When r  n , the formula becomes:
Math 30-2
Permutations & Combinations: Lesson #3
e.g. 2) Evaluate:
a) 9 P4
b)
7
P8
e.g. 3) There are 10 books. In how many ways can 4 of these books be arranged on a shelf?
e.g. 4) A social insurance number (SIN) in Canada consists of a nine-digit number that uses the
digits from 0 to 9. The first digit cannot be 0, 8, or 9 for permanent residents of Canada.
How many SINs are possible:
a) if the digits can be repeated?
b) if the digits cannot be repeated?
c) Which of the above cases uses permutations? Explain.
e.g. 5) Six actors and eight actresses are available for a play with four male roles and three
female roles. How many different cast lists are possible?
Math 30-2
Permutations & Combinations: Lesson #3
e.g. 6) Nine chairs are arranged in a semi-circle. In how many different ways can six people be
seated in the chairs?
e.g. 7) Solve the following equations:
a) n1 P2  56
Assignment:
b)
p. 93-94 #1, 3, 5-10, 12-13, 14a, 15-16
6
Pr  30