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Find the probablity - [Canada 1990 - P1]

Source:

October 4, 2011
probability

Problem Statement

n(n+1)2\frac{n(n + 1)}{2} distinct numbers are arranged at random into nn rows. The first row has 11 number, the second has 22 numbers, the third has 33 numbers and so on. Find the probability that the largest number in each row is smaller than the largest number in each row with more numbers.
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