Alberta Program of Studies (2002)

Topic 5: Permutations and Combinations

General Outcome: Solve problems based on the counting of sets, using techniques such as the fundamental counting principle, permutations and combinations.

Substrand: Chance and Uncertainty

Specific Outcomes

5.1 Use the fundamental counting principle to determine the number of different ways to perform multistep operations. [PS, R]

5.2 Determine the number of linear permutations of n objects taken r at a time, and use this to solve problems. [PS, R, V]

Note: Permutations are restricted to linear permutations only.

5.3 Determine the number of combinations of n distinguishable objects taken r at a time, and use this to solve problems. [PS, R, V]

Note: Combinations are limited to cases involving distinguishable objects only. (Different has been replaced with distinguishable.)

5.4 Determine the number of pathways in a given simple pathway problem. [CN, PS, R, V]

Note: Pathway problems have been separated into simple and compound outcomes.

5.5 Determine the number of pathways in a given compound pathway problem. [CN, PS, R, V]

5.6 Solve problems using the binomial theorem, where the exponent n belongs to the set of natural numbers.

Note: Binomial probabilities are calculated exactly for both small and large numbers of trials.

Deletions:

• Constructing sample spaces
• Classifying events as independent or dependent
• Probabilities of mutually exclusive and complementary events

General Outcome: Model the probability of a compound event, and solve problems based on the combining of simpler probabilities.

Substrand: Chance and Uncertainty

Specific Outcomes:

5.7 Solve probability problems using either permutations and combinations or the fundamental counting principle. [E, PS, R]

Note: Complex probability problems can be solved by either using permutations and combinations or the fundamental counting principle.