  The well-known Erdos-Ko-Rado Theorem states that if F is a family of
k-element subsets of {1,2,...,n} (n>2k-1) such that every pair of elements in F
has a nonempty intersection, then |F| is at most $\binom{n-1}{k-1}$. The
theorem also provides necessary and sufficient conditions for attaining the
maximum. We present elementary methods for deriving generalizations of the
Erdos-Ko-Rado Theorem on several classes of combinatorial objects. We also
extend our results to systems under Hamming intersection.
