Now that's just next level dumbEven in scenarios where you don't choose them.
Yes, it's dumb, but it's plain level dumb for the NNEA (No-NTR Enforcement Agency).
The typical NNEA agent likes to imagine himself as the alpha male that can bang all the girls he wants, and he expects them to be "faithful" to him.
Wanting no male but him having sex is just an ( ε → 0 )-long step further...
So we can safely neglect the infinitesimal term and consider the two terms to be of the same order of dumbness.
Which is already O(n!)
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