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.