4-digit PIN
- Input
- PR(10, 4)
- Expected output
- 10.000
10⁴ possible PINs (0000–9999).
permutations in passwords and security
Permutations in Passwords — Combinatorial Strength
With repetition, PR(n,r) = nʳ. For a 4-digit PIN (0–9): PR(10,4) = 10⁴ = 10,000 combinations.
How alphabet size affects security
- Lowercase only (26): 26⁸ ≈ 208 billion. Adding uppercase (52): 52⁸ ≈ 53 trillion. With symbols (94): 94⁸ ≈ 6 quadrillion.
- Adding one more character multiplies the space by n. Growing n from 26 to 94 roughly doubles the space per character — far less impact than length.
Examples
8-char password (94 symbols)
- Input
- PR(94, 8)
- Expected output
- ≈ 6,1 × 10¹⁵
Computational strength of 8 characters.
Full tool FAQ
A permutation is an ordered arrangement of r elements chosen from a set of n. The order of elements matters: AB and BA are different permutations.
Frequently asked questions
What matters more: length or complexity?
Length has exponential impact (×n per character), while extending the alphabet has less per-character impact. A long lowercase-only password can be stronger than a short one with symbols.
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.