Let $X=\{A_{1},...,A_{n}\}$ be a set of distinct 3-element subsets of the set $\{1,2,...,36\}$ such that (a) $A_{i},A_{j}$ have nonempty intersections for all $i,j$ (b) The intersection of all elements of $X$ is the empty set. Show that $n\leq 100$. Determine the number of such sets $X$ when $n=100$