Set of subsets

Let $X=\{1;2;3;4;5;6;7\}$ , and let $A=\{F_1;F_2;\ldots;F_n\}$ be a collection of distinct subsets of $X$ such that the intersection $F_i\cap F_j$ contains exactly one element whenever $i\ne j$ . For each $i\in X$ ,let $r_i$ be the number of elements in $A$ which contains $i$ .

Suppose $r_1=r_2=1; r_3=r_4=r_5=r_6=2$ and $r_7=4$ .

Find the value of $n^2-n$ .

This is a part of the Set .