# 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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