Case 1
Combination lock
Order matters · repeats OK
Case 2
Podium finish
Order matters · no repeats
Case 3
Pizza order
No order · repeats OK
Case 4
Toppings on one pie
No order · no repeats
Options to choose from
4
how many items in the pool
How many to pick
2
how many slots to fill
Possible outcomes:
16
Each colored dot represents one option. Arrows (→) mean the order matters; plus signs (+) mean it doesn't. Slide the values to see how quickly the number of outcomes grows — and how dramatically the same n and k can produce wildly different counts depending on the rules.
Built as a teaching tool for middle-school probability. The four cases cover every counting problem of this kind that you're likely to meet.