# 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 $$n^2-n$$.

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