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(Multiply probabilities)
P(all different) = (365/365) × (364/365) × (363/365) × ... × (343/365).
That is 23 terms. The numerator is 365 × 364 × ... × 343. The denominator is 365²³.
Using a calculator: P(all different) ≈ 0.493.
P(at least 2 match) = 1 - 0.493 = 0.507, or about 50.7%.
