Permutations and combinations.notebook
May 22, 2013
Section 13.1: Permutations and Combinations
Ways to count total number of outcomes:
1. Basic Counting Principle
2. Permutations(nPr)
3. Combinations(nCr) Basic Counting Principle:
1) must be independent events
2)multiply total number of outcomes for each event
Example: What is the total number of outcomes if you roll a die, flip a coin, and spin an 8 sided spinner?
Example: How many different sandwiches if there are 5 kinds of meats, 6 kinds of cheeses, and 4 types of bread?
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Permutations and combinations.notebook
May 22, 2013
Permutations:
Factorial: n! = n(n­1)(n­2)....(1)
Example: How many ways can 8 people line up for a picture?
The number of permutations of n objects taken r at a time is defined as P(n, r) = n! (n ­ r)!
Calculator: nPr
In a permutation, order is important, such as batting line ups, license plate numbers, phone numbers, etc.
Examples: How many different batting line ups for 9 spots if there are 12 players to choose from?
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Permutations and combinations.notebook
May 22, 2013
Combinations: The number of combinations of n objects taken r at a time is defined as
C(n,r) = n! (n­r)!r!
Calculator: nCr
In a combination problem, order does not matter.
Example: 7 couples are listed on the prom ballot. How many ways are there to choose 4 couples?
Example: 10 names. 6 girls and 4 boys. How many committees of 3 girls and 1 boy can be formed?
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Permutations and combinations.notebook
May 22, 2013
Section 13.2: Permutations with Repetitions and Circular Arrangements
How many arrangements of the word MATH?
How many arrangements of the word ALGEBRA?
The number of permutations of n objects of which p are alike and q are alike is n! p!q!
(divide for each letter that repeats)
How many arrangements of the word MISSISSIPPI?
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Permutations and combinations.notebook
May 22, 2013
How many arrangements of 6 children in a line?
How many arrangements of 6 children in a circle?
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2
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5
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Number of linear arrangements: n!
(A circular arrangement with a fixed point is treated like a linear arrangement.)
Number of circular arrangements: n!
n
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Permutations and combinations.notebook
May 22, 2013
Phone numbers:
a. How many possible 7 digit phone numbers if the first number cannot be 0
b. How many possible 3 digit numbers that contain at least one 2.
c. How many license plate numbers. First three letters, last three are digits.
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Permutations and combinations.notebook
May 22, 2013
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Permutations and combinations.notebook
May 22, 2013
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