*Problem #8*

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

*
* *
* * *
. . .
. . .
. . .
* * ... * *

Let *M*_{k} denote the largest number in the
*k*^{th} row from the top. Find the probability that
*M*_{1} < *M*_{2} < *M*_{3} <
... < *M*_{n}.
**Source: Canadian Mathematical Olmpiad**