Problem #8




A set of n(n + 1)/2 (distinct) numbers is arranged at random in a triangular array:
                         *

                       *   *

                     *   *   *
                     .   .   .
                     .   .   .
                     .   .   .
                 *   *  ...  *   *
Let Mk denote the largest number in the kth row from the top. Find the probability that M1 < M2 < M3 < ... < Mn.

Source: Canadian Mathematical Olmpiad



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