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The hypergeometric distribution describes sampling without replacement: P(X = k) = C(K,k)·C(N−K, n−k)/C(N,n). Unlike the binomial, each draw changes the composition of what remains.
Hypergeometric pmf
P(X = k) = C(K, k)·C(N − K, n − k) / C(N, n)
Mean
E = n·K/N
C(4,2)·C(48,3)/C(52,5) = 6 × 17296 / 2598960 ≈ 0.0399.
When the sample is a small fraction of the population, say under 5%, the difference becomes negligible.