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11

Part of 1992 Poland - First Round

Problems(1)

Six pawns on a chessboard

Source: Poland Math Olympiad 1992 Round 1 #11

6/3/2023
Given is a n×nn \times n chessboard. With the same probability, we put six pawns on its six cells. Let pnp_n denotes the probability that there exists a row or a column containing at least two pawns. Find lim⁡n→∞npn\lim_{n \to \infty} np_n.
probability