Algebra 2 · Unit 11 · Topic 11.2
Permutations and Combinations
For n distinct objects, the number of ordered selections of k without replacement is n!/(n − k)!, while unordered selections number C(n, k) = n!/[k!(n − k)!], with 0 ≤ k ≤ n.
Definition and explanation
For n distinct objects, the number of ordered selections of k without replacement is n!/(n − k)!, while unordered selections number C(n, k) = n!/[k!(n − k)!], with 0 ≤ k ≤ n. Decide whether order matters before selecting a formula.
Worked example
Choose 3 students from 8 for an unordered committee: C(8, 3) = 56. Assigning distinct president, secretary, and treasurer roles instead gives 8 × 7 × 6 = 336 assignments because the roles distinguish order.
Common mistake
Using permutations for an unordered group counts the same group repeatedly.
Key takeaway
For n distinct objects, the number of ordered selections of k without replacement is n!/(n − k)!, while unordered selections number C(n, k) = n!/[k!(n − k)!], with 0 ≤ k ≤ n.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.