Day 1 ­ Counting Principle, Permutations, Combinations.notebook
December 09, 2014
Day 1 ­ Probability and Statistics
Objective: To understand and apply the Counting Principle, Permutations and Combinations (D.4.B)
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Day 1 ­ Counting Principle, Permutations, Combinations.notebook
December 09, 2014
(Note: This can be extended for more than two events.)
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Day 1 ­ Counting Principle, Permutations, Combinations.notebook
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? 3
Day 1 ­ Counting Principle, Permutations, Combinations.notebook
December 09, 2014
3. There are four people waiting to exit an elevator. In how many orders can the people exit? 4
Day 1 ­ Counting Principle, Permutations, Combinations.notebook
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 P . 8 3
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Day 1 ­ Counting Principle, Permutations, Combinations.notebook
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
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Day 1 ­ Counting Principle, Permutations, Combinations.notebook
December 09, 2014
Combinations
Order 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.
C = n!
n r
(n-r)! * r!
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Day 1 ­ Counting Principle, Permutations, Combinations.notebook
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? 8
Day 1 ­ Counting Principle, Permutations, Combinations.notebook
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
9. Using the same scenario from Example 1, 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? (calculator)
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Day 1 ­ Counting Principle, Permutations, Combinations.notebook
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? 10
Day 1 ­ Counting Principle, Permutations, Combinations.notebook
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
b.) 4 fives and 1 other card
c.) 1 queen and 4 cards that are not queens
d.) 5 clubs or 5 diamonds
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Day 1 ­ Counting Principle, Permutations, Combinations.notebook
December 09, 2014
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