Proving an inequality about a set of combinations. Suppose $A$ is a set of $r$ combinations of an $n$ set, with $\alpha \cap \beta \neq \phi$, whenever $\alpha, \beta \in A$. Show that $$|A| \leq \binom{n-1}{r-1}$$ if $r \leq \frac n2$. 
What does this question mean exactly ? Is it the set of all $r$ combinations, such that no two of them are mutually disjoint ?
The hint said to consider $\partial^{n-2r}B$, where $B$ is the set of complements of $A$. I don't know how to apply partial differentiation to combinatorics. Please help.
 A: Let $A=\{A_1,\ldots,A_s\}$ be a family of subsets of $\{1,\ldots,n\}$.  Then, $A$ is said to be an intersecting family if any two elements in $A$ have a nontrivial intersection.  If we also place the restriction that all subsets in $A$ have the same cardinality, say $A$ is an intersecting family of $r$-subsets of $\{1,\ldots,n\}$ , then how large can $A$ be?  
One way to generate an intersecting family of $r$-subsets of $\{1,\ldots,n\}$  is to pick an element, say $1$, to include in each of the $r$-subsets.  The remaining $r-1$ elements can be chosen in ${n-1 \choose r-1}$ ways. Thus, there exists an intersecting family of $r$-subsets of $\{1,\ldots,n\}$ of cardinality ${n-1 \choose r-1}$, namely the set of all $r$-subsets which contain the element $1$.  The Erdos-Ko-Rado theorem asserts that this value is the maximal size  of an intersecting family of $r$-subsets and that every intersecting family of $r$-subsets of maximal size is exactly of the form just mentioned: the set of all $r$-subsets which contain one particular element.  
The symbol $\partial$ is probably the notation for something like the shadow (not the partial derivative).  You can look at your reference (or a text on set-systems) for the exact definition. 
