1
STAT 5112
Spring 2012
Lecture 6
Jan 23, 2012
Jun Xie
Finish Example 13 and 16, more probability propositions, and equally likely outcomes from last post.
2.3 Counting Techniques
Product rule for ordered pairs
Ordered pair: if
O
1
and
O
2
are objects, then the pair (
O
1
,
O
2
) is different from the pair (
O
2
,
O
1
).
Proposition
If the first element or object of an ordered pair can be selected in
n
1
ways, and for each of these
n
1
ways
the second element of the pair can be selected in
n
2
ways, then the number of pairs is
n
1
n
2
.
We will call an ordered collection of
k
objects a
ktuple
.
Product Rule for
k
Tuples
Suppose a set consists of ordered collections of
k
elements (
k
tuples) and that there are
n
1
possible
choices for the first element; for each choice of the first element, there are
n
2
possible choices of the
second element; . . . ; for each possible choice of the first
k
–
1 elements, there are
n
k
choices of the
k
th
element. Then there are
n
1
n
2
· · ·
n
k
possible
k
tuples.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 BUD
 Set Theory, Counting, Probability, Ordered pair

Click to edit the document details