Permutations, Combinations & Factorials Explained
Texas Instruments TI-84 Plus and TI-30XS scientific calculators are staples in algebra, statistics, and precalculus classrooms. This tool replicates their core combinatorics functions — factorials (!), permutations (nPr), and combinations (nCr) — for quick homework verification.
Combinations (nCr) — Order Doesn't Matter
Use combinations when selecting a group where order is irrelevant, like choosing 2 toppings from 5 available flavors. Formula: nCr = n! ÷ (r! × (n-r)!)
Permutations (nPr) — Order Matters
Use permutations when arranging items in a specific sequence, like ranking 1st/2nd/3rd place among 10 runners. Formula: nPr = n! ÷ (n-r)!
Worked Example
5C2 = 5! ÷ (2! × 3!) = 10 | 5P2 = 5! ÷ 3! = 20
Selecting 2 unordered items from 5 gives 10 possible groups; ranking 2 ordered positions from 5 candidates gives 20 possible outcomes.
Common AP Statistics & Probability Uses
- Binomial probability distributions (nCr appears in the binomial coefficient).
- Lottery and card-hand probability calculations.
- Password/PIN combination counting problems.




