A Combinatorial Central Limit Theorem
Let (Y n1,…,Y nn be a random vector which takes on the n! permutations of (1,…, n) with equal probabilities. Let c n(i,j), i,j = 1, …, n, be n real numbers. Sufficient conditions for the asymptotic normality of 
 
$$ S_n = \sum\limits_{i - 1}^n {c_n \left( {i,Y_{ni} } \right)} $$ 
 
are given (Theorem 3). For the special case c n(i,j) = a n(i)b n(j) a stronger version of a theorem of Wald, Wolfowitz and Noether is obtained (Theorem 4). A condition of Noether is simplified (Theorem 1).