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Pre-Calculus 12
Permutations, Combinations, and Binomial Theorem
23. Determine number of combinations of n different elements taken r at a time to solve problems
23.2 Problems involving both permutations and combinations
Permutation or Combination?
The one question that decides it: does the order of selection matter?
What You'll Learn
Ask: does order matter? If yes, use a permutation; if no, use a combination.
Permutation example: choosing a president and VP from 6 people gives 6P2 = 30.
Combination example: choosing a 2-person committee from 6 gives 6C2 = 15.
A combination count is always smaller, since it doesn't count reorderings separately.
Mixed problems apply the order question separately at each stage.
What You'll Practice
1
Calculating poker hands requiring both rank ordering and card selection
2
Determining when order matters for some elements but not others
3
Solving problems with multiple stages using fundamental counting principle
4
Verifying results by comparing total counts across categories
Why This Matters
Mastering problems that combine permutations and combinations prepares you for real-world probability and decision-making scenarios. This skill is essential in statistics, game theory, computer science, and any field requiring sophisticated counting of complex outcomes.
Before You Start — Make Sure You Can:
This Unit Includes
10 Video lessons
Practice exercises
Learning resources
Skills
Permutations
Combinations
Counting Principle
Poker Probability
Multi-step Problems
Order Matters
Selection
NS Curriculum Aligned