Difference between revisions of "Arrangement Restriction Theorem"
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| − | The <b>Arrangement Restriction Theorem</b> is discovered by [[User:aops-g5-gethsemanea2|aops-g5-gethsemanea2]] and is | + | The <b>Arrangement Restriction Theorem</b> is discovered by [[User:aops-g5-gethsemanea2|aops-g5-gethsemanea2]] and is not an alternative to the [[Georgeooga-Harryooga Theorem]] because in this theorem the only situation that is not allowed is that all <math>k</math> objects are together. |
==Definition== | ==Definition== | ||
Revision as of 23:09, 20 December 2020
The Arrangement Restriction Theorem is discovered by aops-g5-gethsemanea2 and is not an alternative to the Georgeooga-Harryooga Theorem because in this theorem the only situation that is not allowed is that all 
objects are together.
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 .
Testimonials
I like this theorem, but not as much as the Georgeooga-Harryooga Theorem or the Wooga Looga Theorem ~ ilp
"Very nice theorem but not as impressive as the Georgeooga-Harryooga Theorem." - RedFireTruck
