Lesson Notes 2-2
Factorial Notation
Factorial notation is a concise representation of the product of consecutive descending
natural numbers: n! = n(n - 1)(n 2) (3)(2)(1). For example, 4! = (4)(3)(2)(1).
Example 1: Evaluate the following.
a) 6!
13!
(b) 4!9
Lesson Notes 2-5
Combinations
It is important to know the difference between a permutation and a combination. The
two formulae are:
nP =
r
n!
(n r)!
n
n!
Cr = =
n
r r!(n r)!
A permutation is an arrangement of a set of objects where order is important.
A
Lesson Notes 2-3
Permutations of Distinguishable Objects
The number of permutations of n different objects taken r at a time is: nPr =
n!
(n r )!
Example 1: Matt has downloaded 10 new songs from an online music store. How many
different 6-song play lists
Lesson Notes 2-4
Permutations of Identical Objects
In lesson 1, we determined the number of arrangements of objects when the objects were
all different (ie. the letters in CLARINET were conveniently different).
Now, lets take any word that has two letters
Lesson Notes 1-2
Intersection & Union of Two Sets
The set of elements that are common to two or more sets is called the intersection. In set
notation, A I B denotes the intersection of sets A and B. For example, if A = cfw_1, 2, 3
and B = cfw_3, 4, 5 then
Lesson Notes 1-1
Types of Sets & Set Notation
QuickTime and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
How could we describe or organize the provinces and territories of Canada?
A set is a collection of distinguishable objects. For
Lesson Notes 2-1
Counting Principles
Counting was fun when you were little, but sometimes there were too many items to
count. In this chapter, you will learn some short cuts to counting. In other words, youll
be counting without actually counting!
Example
Lesson Notes 1-5
Inverses & Contrapositives
A statement that is formed by negating both the hypothesis and the conclusion of a
conditional statement is called an inverse. For example, for the statement If a number is
even, then it is divisible by 2 the in
Lesson Notes 1-4
Conditional Statements
Consider the following two statements:
If Adam is texting, then he is using a cellphone.
If Adam is using a cellphone, then he is texting.
How are the these statements relate to each other? Are they both true?
A c
Lesson Notes 1-3
Venn Diagrams
Part A: Using the word not
The negation of the statement I am going to assign homework tonight would be: I am
not going to assign homework tonight. In Math the symbols for negations are: , , ,
<, >.
Show the following on a n