How do you evaluate 8P5?

Jan 5, 2017

${\textcolor{w h i t e}{}}^{8} {P}_{5} = 6720$

Explanation:

Consider the permutation general case of :" "color(white)()^n P_r = (n!)/((n-r)!)

color(white)()^8 P_5 = (8!)/((8-5)!) =(8xx7xx6xx5xx4xxcancel(3!))/(cancel(3!))

${\textcolor{w h i t e}{}}^{8} {P}_{5} = 6720$

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$\textcolor{b r o w n}{\text{Foot note}}$

The formula for combinations is very similar.

color(white)()^nC_r = (n!)/((n-r)!r!)

Permutations is where the order matters
ie $a , b$ is not the same as $b , a$

Combinations is where the order does not matter
ie $a , b$ is counted the same as $b , a$

So the count of occurrence for combinations is less than the count of occurrence for permutations.