Real-World Combinations Calculator
Calculate the total number of possible combinations for lottery numbers, PIN codes, passwords, and more.
Understand your odds.
Total Combinations
Combinations count the ways to choose items where order does not matter:
C(n, r) = n! / (r! × (n − r)!)
Permutations count arrangements where order matters:
P(n, r) = n! / (n − r)!
Password/PIN combinations (with repetition):
Total = (number of characters)^(length)
Real-world examples:
| Scenario | Combinations |
|---|---|
| 4-digit PIN (0–9) | 10,000 |
| 6-digit PIN | 1,000,000 |
| Powerball (5/69 + 1/26) | 292,201,338 |
| Mega Millions (5/70 + 1/25) | 302,575,350 |
| 8-char password (a–z, 0–9) | 2,821,109,907,456 |
| 8-char password (mixed case + digits + symbols) | ~6.1 quadrillion |
Security implications:
- A 4-digit PIN can be cracked in seconds by a computer
- An 8-character lowercase password: ~minutes to hours
- A 12-character mixed password: centuries to crack
- Each additional character multiplies difficulty exponentially