Goals
Notes
The objective problems of Counting, Part 1 are the following:
I
Notation: n! = n · (n − 1) · (n − 2) · · · 2 · 1 is ”n-factorial.”
Ex: 6! = 6 · 5 · 4 · 3 · 2 · 1 = 720
WeBWorK recognizes ”!”
I
When making a choice, how many objects can you choose from?
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After making a choice, do you need to make more choices?
I
Options Multiply: When making one choice, and then another,
and possibly more, the total number of options multiply.
Options Multiply!
(University of Utah)
Math 1050
1/6
Examples - Counting Part 1
Notes
1.) Dessert We are given two options for ice cream, and then three
options for toppings. We pick one from each. How many total
options are there?
Ice Cream
Chocolate
Vanilla
Toppings
Sprinkles
Hot Fudge
Berries
A 2-by-3 box listing every possible option (there are 2 × 3 = 6):
T
S
F
C C,T C,S C,F
V V,T V,S V,F
(University of Utah)
Math 1050
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Examples - Counting Part 1
Notes
If there are m options for one choice, then n options for another
choice, then there are m · n total options. This extends if several
choices appear with various options.
2.) A litter of puppies has five puppies. The owners have decided to
name them Alex, Bailey, Charleston, Dakota, and Emo. All they have
to do is decide which puppies receive each name. How many different
options are there for which puppy is given which name?
(University of Utah)
Math 1050
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Examples - Counting Part 1
Notes
3.) A national magazine describes 10 U.S. cities to visit. You want to
plan a vacation to one of the cities, and you can travel during May,
June, July, or August. You can stay at either a hotel, hostel, or
campsite. How many vacations do you have to choose from?
(University of Utah)
Math 1050
4/6
Examples - Counting Part 1
Notes
Count the options to make the first choice, n. Then count the
remaining options to make the next choice (n − 1), and so on.
Multiply the options to find the number of different ways to choose
and order k objects from a set of n objects.
4.) A volleyball team roster has 11 players. There are six different
positions on the court. How many different ways can a coach select
to fill the six positions?
(University of Utah)
Math 1050
5/6
Examples - Counting Part 1
Notes
5.) There are 10 guests at a mystery party. One person needs to
guard the entrance, one person needs to guard the kitchen, and one
person needs to guard the hallway. How many different ways can
those three places be guarded by the 10 people at the party?
(University of Utah)
Math 1050
6/6