A walkthrough, end to end.
- 1
Enter n (total items) and r (chosen).
- 2
The calculator returns nPr (permutations: ordered arrangements) and nCr (combinations: unordered selections).
- 3
Both n! and r! are shown as bonus.
Permutations vs Combinations
Permutations: order matters — nPr = n! / (n−r)!. Combinations: order doesn't matter — nCr = n! / (r!(n−r)!). Lottery picks are typically combinations; race finishing positions are permutations.
What you can do with this.
Lottery odds
Pick 6 from 49 → C(49, 6) = 13,983,816 combinations. Probability of winning = 1 in 14M. The calculator gives the count directly.
Password strength
Permutations of 10 characters from 26-letter alphabet: P(26, 10) = 1.92 × 10¹¹. Adding case + digits explodes the count further. Foundation of password-strength estimation.
Tournament brackets / standings
Order positions matter — use permutations. 8 teams with 3 podium positions: P(8, 3) = 336 possible podium orders.
Committee selection
Pick 5 from 12 (any order, no repeats) = C(12, 5) = 792 combinations. Useful for committee, jury, team selection.
Pizza topping combinations
Choose 3 toppings from 8: C(8, 3) = 56 unique combinations. Pizza shops use this math implicitly when sizing topping options.
Card games / poker hands
5-card hand from 52 cards: C(52, 5) = 2,598,960 distinct hands. Foundation of poker probability calculations.
Birthday paradox
Probability that 23 people share a birthday > 50%. Computed via complement of 'all 23 different birthdays' which uses permutations. The calculator supports the underlying math.
Factorial size
10! = 3.6M; 20! ≈ 2.4 × 10¹⁸; 50! ≈ 3 × 10⁶⁴. JavaScript loses precision around n = 18; calculator handles up to n=170 (Infinity above).
P&C calculator 2026 — what's current
Foundational combinatorics. AI tools handle reliably. Calculator wins for speed and verification.
Frequently asked.
If order matters (race positions, password characters, arrangement) → permutation. If order doesn't matter (lottery, committees, hand of cards) → combination.
Factorials overflow ~170! → Infinity in JavaScript Number. The calculator returns Infinity above this. For larger numbers, use BigInt or specialized libraries.
nC0 = 1 (one way to choose nothing). Same for nCn (one way to choose everything). Edge cases the formula handles correctly.
No. Calculations run entirely in your browser.