Difference between revisions of "Arrangement Restriction Theorem"
(Created page with "The Arrangement Restriction Theorem is discovered by aops-g5-gethsemanea2 and is an alternative to the Georgeooga-Harryooga Theorem. ==Definition== If there are <math>n</...") |
|||
| Line 1: | Line 1: | ||
| − | The Arrangement Restriction Theorem is discovered by aops-g5-gethsemanea2 and is an alternative to the [[Georgeooga-Harryooga Theorem]]. | + | The <b>Arrangement Restriction Theorem</b> is discovered by [[User:aops-g5-gethsemanea2|aops-g5-gethsemanea2]] and is an alternative to the [[Georgeooga-Harryooga Theorem]]. |
==Definition== | ==Definition== | ||
Revision as of 06:48, 20 December 2020
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 .
