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Permutations & Combinations
· History📜 History & Discovery
The Sanskrit scholar Pingala (~200 BCE) used combinatorial ideas to count Vedic metre patterns. Indian mathematician Mahavira (850 CE) gave explicit formulas for nPr and nCr. Blaise Pascal (1654) systematised combinations through his famous triangle. Leibniz independently developed combinatorics. Euler later connected P&C to graph theory and topology.
⚡ 2026 Update
Every modern password rule is a P&C calculation. An 8-character password with 94 printable ASCII characters has 94⁸ ≈ 6.1 quadrillion combinations — even at a billion brute-force attempts per second that takes ~70 days. Add one more character and you push it past 18 years.