Six points in a plane be joined in all possible ways by indefinite straight lines, and if no two of them be coincident or parallel, and no three passs through the same point. (with the expectation of the original 6). The number of distinct points of intersection is equal to

Question

$\begin{array}{1 1} 105 \\ 45 \\ 51 \\ \text{none of these} \end{array} $