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Lesson 1: Combinations and Permutations
Curriculum Connections
British Columbia Ministry of Education Curriculum of Mathematics Grade 10 Principles of Mathematics: statistics and Probability: Chance and Uncertainty:C10 solve probability problems involving permutations, combinations, and conditional probability:
- Use factorial notation to determine different ways of arranging n distinct objects in a sequence
- Evaluate a given factorial using technology
- Simplify a fraction that contains a factorial in both the numerator and denominator
- Use factorial notation to solve given problems
- Determine the number of permutations of n different objects taken r at a time, and use this to solve problems
- Calculate the number of permutations of n things taken r at a time using nPr
- Obtain the solution to a given problems involving a single case or constraint
- Determine the number of combinations of n different objects taken r at a time, and use this to solve problems
- Write nCr using factorial notation
- Calculate the number of combinations of n things taken r at a time using nCr
2.1 recognize the use of permutations and combinations as counting techniques with advantages over other counting techniques (e.g., making a list; using a tree diagram; making a chart; drawing a Venn diagram), distinguish between situations that involve the use of permutations and those that involve the use of combinations (e.g., by considering whether or not order matters), and make connections between, and calculate, permutations and combinations
2.2 solve simple problems using techniques for counting permutations and combinations, where all objects are distinct, and express the solutions using standard combinatorial notation [e.g., n!, P(n, r), ( )]
Learning tools such as manipulatives and technologies are important supports for teaching and learning mathematics…the representation of mathematical ideas using manipulatives helps students to:
- See patterns and relationships
- Make connections between the concrete and the abstract
- Test, revise, and confirm their reasoning
- Remember how they solved a problem
- Communicate their reasoning to others.
Technology connection
Many calculators have a factorial key n! To use, enter n then press n! and then enter =
There is also a nPr key and nCr to calculate permutations and combinations. Enter n then enter nPr or nCr, enter r and then =
Many calculators have a factorial key n! To use, enter n then press n! and then enter =
There is also a nPr key and nCr to calculate permutations and combinations. Enter n then enter nPr or nCr, enter r and then =
