How many?

Suppose there are $n$ students on the council. If Maria is to be chosen, there are then $\dbinom{n-1}{2}$ ways to choose the other two members. Since in general there are $\dbinom{n}{3}$ ways to choose three members, we then need to find $n$ such that

$\dfrac{\dbinom{n-1}{2}}{\dbinom{n}{3}} = \dfrac{1}{2} \Longrightarrow \dfrac{\dfrac{(n - 1)(n - 2)}{2}}{\dfrac{n(n - 1)(n - 2)}{6}} = \dfrac{1}{2} \Longrightarrow 6(n - 2) = n(n - 2) \Longrightarrow n^{2} - 8n + 12 = 0 \Longrightarrow (n - 6)(n - 2) = 0$ .

Now since we are to choose three members we know that $n \ge 3$ , and thus $n = \boxed{6}$ .