Question

How do you evaluate 8P5?

Answer 1

`color(white)()^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!))`

`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.