New in Wolfram Mathematica 7: Industrial-Strength Boolean Computation  previous | next 
Count the Number of Instances Satisfying a Boolean Expression
The number of instances of 3000 variables with between 1000 and 2000 variables True.
In[1]:=

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vars = Array[x, 3000];

SatisfiabilityCount[

 BooleanCountingFunction[{1000, 2000}, 3000] @@ vars, vars]
Out[1]=