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The binomial distribution models the number of successes in n independent trials with fixed probability p per trial. P(X=k) = C(n,k) × pᵏ × (1−p)^(n−k). Mean = np; variance = np(1−p).

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1. 1P(X=k) = C(n,k) × pᵏ × (1−p)^(n−k)
2. 2C(n,k) = n! / (k! × (n−k)!) — combinations
3. 3Applies when: fixed n, binary outcome, constant p, independent trials

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