A small draw bowl with unnumbered balls and an unordered selection tray. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
Count unordered tickets first
In a teaching lottery that draws two distinct numbers from five, an unordered two-number ticket has C(5,2) = 10 possibilities. Fix one selected ticket. Exactly one match requires choosing one of its two numbers and one of the other three numbers. There are C(2,1)C(3,1) = 6 favorable draws, so the probability is 6/10 = 60%.
Why the counts multiply
For a pool N, r selected numbers and r drawn numbers, exactly k matches uses C(r,k) choices from the selected set and C(N−r,r−k) choices from outside it. Divide their product by C(N,r). The draw is without replacement, so a fixed-probability binomial model does not describe these dependent within-draw selections.
Check every possible match count
| Matches in the two-from-five example | Favorable draws | Probability |
|---|---|---|
| 0 | 3 | 30% |
| 1 | 6 | 60% |
| 2 | 1 | 10% |
The three disjoint match categories sum to one. This is a useful check on both the counting model and the meaning of “exactly.” A prize for at least one match would combine the last two categories, rather than use the exactly-one answer.
Keep prize rules outside an unsupported model
The Lottery Calculator handles one unordered ticket with equal selected and drawn counts, plus an optional separate independent bonus pool. It does not infer actual prizes or combine overlapping tickets. Read the bonus-pool distinction before multiplying probabilities. For hands-on arithmetic, the Lottery Quiz uses deliberately small examples rather than financial recommendations.
Check the model behind your result
Use the Lottery Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26