The second moment method has been fruitfully combined with conditioning by several authors, for example Robinson and Wormald \cite\RWcubic, \cite{\RWregular} and Frieze and Janson \cite\SJF. We try to give a general exposition of this method, and of its relation to approximations of
random variables by simpler variables. We discuss several examples where the method has been used in different forms.


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