my instinct for approaching the problem:

    C(6,2) / C(n,2) = 1/3

(where C(n,k) is n choose k)

    15 / [n(n-1)/2] = 1/3
    30 / n(n-1) = 1/3
    n(n-1) = 90

I probably wouldn't have done that in high school, though.