Curriculum placement
Precalculus. This describes the skill, not a learner estimate.
Permutations and combinations
Count ordered and unordered selections to compute compound probabilities
Problem types
- Count ordered arrangements
- Count unordered selections
- Probability by counting selections
Builds on
- Probability of compound events
- Operations on rational expressions · Useful idea
The number of combinations is a ratio of factorials that simplifies by canceling common factors.
Leads to
- The binomial theorem · See it applied
The coefficient of the term with k factors of a in (a + b)ⁿ counts the ways to choose which k of the n factors give a. That count is the combination C(n, k).
- A procedure that gives each outcome a fair chance · See it applied
A fair random choice among arrangements or groups gives each of the counted outcomes the same probability.
- A distribution from a sample space · See it applied
Counting arrangements gives the numbers of ways behind binomial and other theoretical probabilities.
Related skills
- Finding a conditional probability · Shared foundations
- Unions, intersections, and complements · Shared foundations
- Defining a random variable · Shared foundations
Open the interactive map to explore lessons and skill connections.