Tukuk-OS🧮 Combination Calculator
ℹ️ What this tool does & how it works
The gap between a combination (which items — order ignored) and a permutation (which items and which order) is the most-miscounted idea in everyday probability: 5 cards from 52 are 2,598,960 hands, but 2·431,840,640 ordered deals. Both live here with BigInt exactness — every product and division is an integer operation, so the answer is provably right, not floating-point approximate.
Why every second lottery ticket feels overdue
Independent draws have no memory — once in 13,983,816 (the classic 6-from-49 jackpot, C(49,6), shown exactly by this page) is a per-draw probability, not a schedule. The human pattern-matching brain that reads a long gap as a due win is the same one that reads permutations as combinations and miscounts the real odds by a factor of 720 (that is 6!). Getting the integer right is the whole defence: 2,598,960 hands you can check; "about 2.6 million" is where the mistakes hide.