Permutations vs. Combinations — Semester Planner

What’s the difference?
• Permutation (order matters): Arrangements where the sequence is important.
Use when Slot 1, Slot 2, … are distinct (e.g., Monday 8am ≠ Tuesday 10am).
• Combination (order doesn’t matter): Selections where only the set of chosen items matters.
Use when you just need a group (e.g., any set of 4 courses, regardless of times).

Formulas
Permutations without repetition: P(n,k) = n × (n−1) × … × (n−k+1) = n!/(n−k)!
Combinations: C(n,k) = P(n,k)/k! = n! / (k!(n−k)!)

How this page uses them
• Toggle Order matters = ON → we count P(n,k) (choosing courses into distinct time slots).
• Toggle Order matters = OFF → we count C(n,k) (just picking any set of k courses).

Example: choose k = 4 courses from n = 6 available. If “order matters” (e.g., time slots), we count permutations. If “order doesn’t matter”, we count combinations.

Total available courses (n)

Courses to take (k)

Order matters (Permutation) Permutation (order matters)

Available courses

Click a course to place it into the next free slot (no repetition). Click a filled slot to put it back.

Semester slots (k)

P(6,4) = 6 × 5 × 4 × 3 = 360 C(6,4) = 15

For permutations: P(n,k) = n × (n−1) × … × (n−k+1) = n!/(n−k)!
For combinations: C(n,k) = P(n,k)/k! = n! / (k!(n−k)!)

Enumerates when total ≤ 500 items.