lew@ihuxr.UUCP (09/27/83)
Jim Balter posed the following: "The squares of a chessboard are numbered randomly, all differently. What is the probability that at least one of the squares is both the maximum in its row and the minimum in its column?" Having learned my lesson from Jim on mutually exclusive events, I noticed that a square which is both a row max and column min must be unique. (If it's a column min, it must be less than every other row max.) Therefore, the probability of SOME square meeting the condition is the sum of the probabilities of each square meeting the condition. For the nth ranked square, the probability is the number of ways to fill in the rest of the row with numbers less than n, times the number of ways to fill in the column with numbers greater than n, divided by the number of ways to fill in the row and column with any numbers. From this I get: P = sum n=8,57 of C(n-1,7) * C(64-n,7) / ( C(63,7) * C(56,7) ) I get P = .0012432 from this. Is this right? Lew Mammel, Jr. ihuxr!lew