How do you evaluate 8P5?

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Answer 1 · 2017-01-05T13:59:54

$color(white)()^8 P_5 =6720$

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

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

$color(white)()^8 P_5 =6720$

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$color(brown)("Foot note")$

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.