Calculate combinations (nCr), permutations (nPr), factorials, and binomial probability. Ideal for statistics coursework, lottery odds, and discrete probability problems.
Combinations: C(n,r) = n! ÷ (r! × (n−r)!)
Permutations: P(n,r) = n! ÷ (n−r)!
Factorial: n! = n × (n−1) × ... × 2 × 1; 0! = 1
Example: Choosing 3 from 10. C(10,3) = 120 (unordered). P(10,3) = 720 (ordered).
Permutations count arrangements where order matters (nPr = n! / (n−r)!). Combinations count selections where order does NOT matter (nCr = n! / (r! × (n−r)!)).
Binomial probability gives the chance of exactly k successes in n independent trials, each with probability p: P(X=k) = C(n,k) × pᵏ × (1−p)^(n−k).
n! (n factorial) is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1.
In a lottery picking 6 from 49, the number of combinations is C(49,6) = 13,983,816 — so your odds of winning the jackpot are 1 in ~14 million.
P(event does NOT happen) = 1 − P(event happens). This is useful when calculating 'at least one' probabilities.