# Venn Diagrams Review Of the girls at a high by davebusters

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```									Venn Diagrams Review:
Of the 615 girls at a high school, 400 play sports in the fall,
225 play sports in the winter, and 365 play sports in the
spring. 175 play in both the fall and the winter. 125 play in
both the winter and the spring, and 275 play in both the fall
and the spring. 75 play all season. How many of the girls
don't play a sport at all?

Create a venn diagram:
Fall                  Winter
Fill in starting with the
overlapping regions:

All
Spring
girls

Set Notation:     Four sets representing:       spring sports
fall sports
winter sports
"the universe"
Everything NOT in the spring
set
Fall            Winter
The union of the spring and fall
sets
The intersection of the spring and
winter sets
The intersection of the winter set
and what's NOT in the fall set.                                    All
Spring
girls

Inclusion-Exclusion Principle:

A                   B

U
Practice: In a survey of 52 Analysis students, 40 liked
classic rock, and 17 liked rap. 5 said they didn't like either.
How many liked classic rock but not rap?

Wassamatter U. has 1000 students. Let F = the set of
college freshmen and M = the set of math majors. The sets
are shown in the diagram below. For each of the sets
below, describe the members of the set, and tell how many
members it has:
U
F                   M
285     15      50

1000
The Multiplication Principle:

If an action can be performed in n1 ways, and for each of
those ways, another action can be performed in n2 ways,
then the two actions can be performed together in n1n2
ways.

Example: You have 3 fake moustaches and 5 wigs.
How many different disguises can you make, assuming
your disguise involves one of each?

How many ways are there to arrange 7 people into a
line?

digits followed by 3 letters?

Why do the numbers decrease in the line example, but
not in the license plate example?
How many ways are there to rearrange the letters in the
word Bargle?

The factorial button on your calculator:

The !
"factorial"        to PRB...     button

Note: By definition, 0! =

How many ways are there to pick a president and a vice-
president from a class of 300 people?

How many 5-digit even numbers can be made from the
digits 1, 4, 5, 7, 8, and 9?
Homework: Assignment 52

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