Major Probability Question 2.

Discrete Mathematics Level pending

Three persons \(A,B,C\) play the following game: a subset with \(k\) elements of the set \(\{1,2, ... , 1986\}\) is selected randomly, all selections having the same probability. The winner is \(A, B, \) or \(C\) according to whether the sum of the elements of the selected subset is congruent to \(0, 1, \) or \(2\) modulo \(3\). Which of the values listed for \(k\) gives \(A,B,C\) an equal probability of winning?

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