# Difference between revisions of "Arrangement Restriction Theorem"

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So, by complementary counting, we get <math>n! - (n - k + 1)!k!</math>. | So, by complementary counting, we get <math>n! - (n - k + 1)!k!</math>. | ||

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+ | ==Testimonials== | ||

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+ | I like this theorem, but not as much as the Georgeooga-Harryooga Theorem or the Wooga Looga Theorem ~ ilp |

## Revision as of 09:40, 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