1. April 12, 2012
9.6 Counting
Principles
Essential Question:
How do you count the number of ways in which an event
can occur?
Objectives:
- Solve simple counting problems
- Use the Fundamental Counting Principle
- Use permutations and combinations to solve counting
problems.
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2. April 12, 2012
The Fundamental Counting
Principle
Determines:
If one group has M choices and another
group has N choices, the total number
of choices is:
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3. April 12, 2012
Keep in mind:
1)
2)
3)
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4. April 12, 2012
Using the FCP:
Ex. 1) A combination lock will open when the right
choice of 3 numbers (from 1-30, inclusive) is selected.
How many different lock combinations are possible?
Ex. 2) In a certain state, each automobile license
plate consists of two letters followed by a four-digit
number. How many distinct license plate numbers can
be formed?
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5. April 12, 2012
Ex. 3) Problems 1-4 on a quiz are multiple choice (A-E)
and problems 5 and 6 are true/false. How many ways
can the quiz be answered?
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6. April 12, 2012
Combination or Permutation?
Combination: Order _________
formula:
Permutation: Order _________
formula:
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7. April 12, 2012
Ex. 4) How many ways can eight children line up in a row?
The number of permutations of
"n" elements is:
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8. April 12, 2012
Eight horses are racing at the Belmont Stakes.
Ex. 5) How many different ways can all the horses finish?
Ex. 6) How many ways can the horses finish 1st, 2nd, or
3rd?
Ex. 7) How many ways can a horse finish in the top 3?
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9. April 12, 2012
Ex. 8) A high school baseball team has 15 players. If two
players are selected to be co-captains, how many
different ways can the co-captains be chosen?
Ex. 9) A 5-person dodge ball team is to be made up of 3
teachers and 2 students. If 6 teachers and 10 students
volunteer to be on the team, how many different teams
are possible?
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10. April 12, 2012
Distinguishable Permutations
How many different combinations are
possible with 3 letters?
Write the possible arrangements of MAT.
Write the possible arrangements of MOM.
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11. April 12, 2012
Calculating Distinguishable
Permutations
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12. April 12, 2012
Ex. 10) Find the number of distinguishable permutations of
the group of letters in MISSISSIPPI
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13. April 12, 2012
Assignment:
9.6 p. 698 #11-27 (odd), 37-43
(odd), 47, 49, 53
Quiz #5 on Monday
Grading Period Ends (so Moodle!)
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