Arrangement Restriction Theorem
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The Arrangement Restriction Theorem is discovered by aops-g5-gethsemanea2 and is an alternative to the Georgeooga-Harryooga Theorem.
Definition
If there are 
objects to be arranged and 
of them should not be beside each other altogether, then the number of ways to arrange them is 
.
Proof/Derivation
If there are no restrictions, then we have 
. But, if we put objects beside each other, we have 
because we can count the objects as one object and just rearrange them.
So, by complementary counting, we get .
