DEMONSTRATION MINILESSON

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DEMONSTRATION MINI-LESSON

• by
• Phillip Antonino

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OVERVIEW

• Task Stream separate handout
• Course Discrete Mathematics
• Lesson Combinatorics
• Mini-Lesson Calculating combinations and
  permutations

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DISCRETE MATHEMATICS

• Discrete Mathematics introduces students to the
  mathematics of networks, social choice, and
  decision making. The course extends students
  application of matrix arithmetic and probability.
  Applications and modeling are central to this
  course of study.
• Discrete Mathematics is replacing Analysis.

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COMBINATORICS

• Combinatorics is the study of combinations and
  permutations calculations. It provides a useful
  foundation in the study of probability,
  statistics, and computer science.

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COMBINATIONS AND PERMUTATIONS

• Combination specific number of arrangements
  where order is not important
• Permutation specific number of arrangements
  where order is important

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EXAMPLES

• COMBINATION
• Two job openings where the jobs are the same.
• How many possible solutions are there if 4 people
  apply?
• Your answer ______

• PERMUTATION
• Two job openings where there are two distinct
  jobs.
• How many possible solutions are there if 4 people
  apply?
• Your answer ______

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FORMULAS

• Combinations
• n!/(n-r)!r!
• r things chosen from n things when order is not
  important
• Previous example
• 4!/(4-2)!2! 6

• Permutations
• n!/(n-r)!
• r things chosen from n things when order is
  important
• Previous example
• 4!/(4-2)! 12

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TI 83 PLUS DEMONSTRATION

• Math option row 4, column 1
• Probability option PRB
• Permutation formula option 2
• Combination formula option 3
• Factorial formula option 4
• Find 6!
• Find Permutation of n6, and r3
• Find Combination of n6, and r3
• Why is the Permutation greater than the
  Combination in this case?

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IN-CLASS PROBLEM 1

• In how many ways can a club with 10 members
  choose a 3-person governing council?

• In how many ways can a club with 10 members
  choose a president, a vice president, and a
  treasurer?

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IN-CLASS PROBLEM 2

• Of the 12 players on a schools basketball team,
  the coach must choose 5 players to be in the
  starting lineup. In how many ways can this be
  done if
• the playing positions are considered?
• the playing positions are not considered?

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APPLICATIONS

• Telephone number combinations
• License plate combinations
• Gambling
• Insurance Company
• Food Industry
• Clothing

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SUMMARY

• Combination order is not important
• Permutation order is important
• TI 83Plus helpful when solving higher level
  problems
• Questions???