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Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
Day 1 Probability and Statistics
Objective: To understand and apply the Counting Principle, Permutations and Combinations
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
Apple has come out with two new products recently, the iPhone 6 and the iPhone 6+.They come with 3 different colors (silver, grey and gold) and three different memory options(16GB, 64GB, and 128GB).
How many different iPhone 6s are there?
6
silver
grey
gold
16GB
64GB
128GB16GB
16GB
64GB
64GB
128GB
128GB
6+
silver
grey
gold
16GB
64GB
128GB16GB
16GB
64GB
64GB
128GB
128GB
This is called a tree diagram, but we have a quicker way tocome up with this number. It is called the counting principle.
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Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
(Note: This can be extended for more than two events.)
Use the fundamental counting principle to find the number of choices for sundae of your dreams.You can choose one flavor of ice cream, one candy topping and one dessert topping. Your choices are for ice cream, vanilla, chocolate, or strawberry. Your choices for candy topping are M&M's, Heath, and Butterfinger. Your choices for dessert toppings are Hot Fudge, Magic Shell or Caramel.
3 x 3 x 3
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
Let's use the Fundamental Counting Principle:
1. You are framing your prom picture. The frames are available in twelve different styles. Each style is available in fiftyfive different colors. You want a blue mat board which is available in eleven different shades. How many different ways can you frame your prom picture?
2. The standard configuration for a Texas license plate is one letter followed by two digits followed by three letters.
a) How many different license plates are possible if the letters and digits can be repeated?
b) How many different license plates are possible if letters and digits CANNOT be repeated?
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
3. There are four people waiting to exit an elevator. In how many orders can the people exit?
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
4. There are 8 sprinters running the 100 meter dash. How many ways can the runners finish the race?
5. If the top three sprinters earn medals, how many different ways are there to medal?
The answer to this can be called the number of permutations of 8 objects taken three at a time. It is denoted at 8P3 .
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
6. You are burning a demo CD for your band. Your band has 12 songs stored on your computer. However, you can only put 4 songs on the demo. In how many orders can your burn 4 of the 12 songs on the CD?
7. Permutations with Repetition:Find the number of distinguishable permutations of the letters in:
a) MISSOURI b) ALGEBRA c) MISSISSIPPI
MISSOU
RI
MISSIS
SIPPI
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
CombinationsOrder does not matter!!
What is a combination? A combination is a selection of r objects from a group of n objects when order is not important.
n Cr = n! (n-r)! * r!
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
Examples
8. Parents have ten books that they can read to their children for Book It this week. Five of the books are nonfiction and five of the books are fiction. If the order in which they read the books is not important, how many different sets of four books can they choose?
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
Multiple Events
*When finding the number of ways both an Event A AND Event B can occur, you multiply.
*When finding the number of ways that Event A OR Event B can occur, you add
Ex: Suppose Tiny Tim is shopping with his mother. She has agreed to let him buy one Transformer and two Captain Marvel action figures. If there are 8 different Transformers to choose from and 10 different Captain Marvel action figures, how many different combinations are possible.
Tiny Tim's mom found out that Bob Cratchit, Tiny's dad, had lost his job. She told Tiny that he could choose either 1 Transformer, or two Captain Marvel action figures. How many different combinations are possible?
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
9. Using the same scenario from Example 8, in how many groups of four books are all the books either nonfiction or fiction?
10. The Student Senate consists of 6 seniors, 5 juniors, 4 sophomores, and 3 freshmen.
a. How many different committees of exactly 2 seniors and 2 juniors can be chosen? (by hand)
b. How many different committees of three sophomores or three freshman can be made?
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
11. A standard deck of 52 playing cards has 4 suits with 13 different cards in each suit.
a. If the order is not important in which the cards are dealt, how many different 5 card hands are possible?
b. In how many 5 card hands are all 5 cards the same color?
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014
12. Using the standard deck of playing cards, how many different 5 card hands are possible if you want:
a.) 3 queens and 2 other cards not queens.
b.) 4 fives and 1 other card
c.) 1 queen and 4 cards that are not queens
d.) 5 clubs or 5 diamonds
Day 1 Counting Principle, Permutations, Combinations 2.notebook
Stat day 1 notes
December 09, 2014