🎲 Discrete Mathematics & Probability
Combinations & Permutations Calculator ($nCr$ & $nPr$)
Compute combinations ($nCr$), permutations ($nPr$), factorials ($n!$), repetitions, and probability event odds for games of chance and statistical sampling.
🃏 5-Card Poker Hand (52C5 = 2.59M)
🎟️ Powerball 5 White Balls (69C5 = 11.2M)
🔢 4-Digit PIN (10P4 = 5,040)
🥇 Olympic Podium Top 3 (8P3 = 336)
Set & Subset Sizes
Combinations (nCr — Order Does Not Matter)
2,598,960
Permutations ($nPr$)
311,875,200
Order Matters
Permutations w/ Rep ($n^r$)
380.2 Million
Subset Factorial ($r!$)
120
💡 Formula Calculation:
$$\binom{52}{5} = \frac{52!}{5! \times (52-5)!} = \frac{52 \times 51 \times 50 \times 49 \times 48}{120} = 2,598,960$$
Combinatorics Mathematics
Key counting principles in discrete mathematics and statistics:
- Permutations without Repetition ($nPr$): $$nPr = \frac{n!}{(n-r)!}$$
- Combinations without Repetition ($nCr$): $$nCr = \binom{n}{r} = \frac{n!}{r!(n-r)!} = \frac{nPr}{r!}$$
- Permutations with Repetition: $$N = n^r$$
- Combinations with Repetition: $$\binom{n+r-1}{r} = \frac{(n+r-1)!}{r!(n-1)!}$$