# Questions on systems of distinct representatives

I have two problem on systems of distinct representatives, but I have nopt solved it yet. Please feel freely helping me solve these problems.

1-Suppose $A_{i} \in \lbrace{1,2...,n\rbrace}$ is a collection of $n$ subsets such that $|A_{i}\cap A_{j}|=1$. Does this collection have an SDR?

2-Let $A_{1},...,A_{n}$ be finite set. Show that if : $\sum_{1\le i<j\le n}^{}\dfrac{|A_{i}\cap A_{j}|}{|A_{i}||A_{j}|} < 1$ then the set $A_{1},...,A_{n}$ have a system of distinct representatives.

Thanks !

-
Do you have any theorems on SDRs that you might be able to apply? –  Gerry Myerson Nov 7 '11 at 5:37
Oh, and I think you want $A_i$ in the first question to be a subset, not an element. –  Gerry Myerson Nov 7 '11 at 5:38