PreCal 12
Unit 6: Permutations and Combinations Lesson 1
NOTES:
I. A) Using Counting Principles to Solve Problems: counting methods are used to count members of
a specific set and the outcomes of an event.
Eg.1: There are 2 styles of kitchen cabinets and 3 finishes that cabinets come in. How many different
finished kitchen cabinets are possible?
Solution:
B)

Definition of the Fundamental Counting Principle
Suppose an event K can occur in k ways and after it has occurred, event M can occur in m ways.
Therefore the number of ways in which K and M can occur is k  m ways.
Eg.
A) How many different 3-digit numbers can be made using seven digits 1,2,3,4,5,6,7 without
repetition.
B) How many 3-digit numbers are even?
C) How many 3-digit numbers are odd?
D) How many 3-digit numbers are greater than 300?
Solution:
C)
Factorial Notation: 4!
Generally:
n!
Eg. Show that:
A) 5!4! 6  4!
Solution:
Read as 4 factorial
read as n factorial
=
=
4  3  2 1  24
n  (n  1)  (n  2)  ...  2  1  n!
B)
(k  1)! k! (k  2)k!
Solution:
D)

Explain the Additive Counting Principle which Implies “OR” statements
When 2 events occur independently, you add their results to get the total number of ways an event
can occur. This involves drawing up separate cases and adding to get the total number.
Eg. 1 How many whole numbers are less than 300? (no repetitions)
Solution:
Eg. 2 How many different 3-digit numbers that are even and greater than 300 can be formed using
1,2,3,4,5,6,7?
Solution:
Assignment: Worktext: p. 689-694 #3-16 MC #1-3