MathDB

37

Part of 1987 IMO Longlists

Problems(1)

Probablity is greater than 6/{(n-2)^3}

Source:

9/5/2010
Five distinct numbers are drawn successively and at random from the set {1,⋯ ,n}\{1, \cdots , n\}. Show that the probability of a draw in which the first three numbers as well as all five numbers can be arranged to form an arithmetic progression is greater than 6(n−2)3\frac{6}{(n-2)^3}
probabilityarithmetic sequencecombinatorics unsolvedcombinatorics