Finite Mathematics Lesson 6

Section 5.4 Section 5.5

Chapters 5.4 - 5.5

This may be a little harder.  I recommended writing out sample spaces by hand or even drawing pictures to help you see how to count.  

Counting
Counting is a general term that describes a method for counting objects in a set.  We may want to count the number of objects in a set or the numbers of ways the objects can be arranged.  We could also count the number of possible poker hands that could be dealt given a single deck of cards.   Many of these type of counting problems are much to difficult to use a trail and error approach.  Could you image actually trying to count out each possible hand of poker?.  Chapter 5 will explore different counting techniques.

Course Notes

Section 5.4   The Multiplication Principle

Generalized Multiplication Principle
Suppose a task consists of t operations perform consecutively.  Suppose OPERATION 1 can be performed in m1 ; for each of these , OPERATION 2 can be performed in m2 ; for each each of these, OPERATION 3 can be performed in m3 ; and so forth.  The the task can be performed in   m1 m2 m3  mt   ways. 

Example
A women has 4 blouses, 3 skirts and and 5 pairs of shoes.  Assuming the woman does not care what she looks like, how many different outfits can she wear?

Example - A classic Problem
License plates for cars have to be unique. If a license plate contains 6 characters: 2 letters followed by 4 digits  i.e.  we2354  etc..

What if letters were allowed to repeated but numbers were not allowed to be repeated?

Example
Fred has 10 different pairs of shoes.  In how many ways can Fred put on a pair of shoes that do not match.

Let's look at this problem two ways....The first way is to count all the combinations. 

The second way is much easier, but harder conceptionally. Apply the multiplication rule...

When you are ready, click here for the assignment for this section.

Section 5.5   Permutations and Combinations

When you are ready, click here for the assignment for this section.

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