How do you evaluate 5P5?

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Answer 1 · 2017-06-18T21:45:36

The simple answer is 120.

$"_5P_5$ is the number of ways of picking 5 objects out of a group of 5 objects, where order matters.

Whenever you select ALL of the objects and order matters, the formula for $"_nP_n$ is $n!$ .

Since $5! = 5(4)(3)(2)(1) = 120$ , that answers the question at hand.

In general, though, if you are only selecting r of the objects -- not necessarily all of them:

$"_nP_r = (n!)/((n-r)!)$

Answer 2 · 2017-06-18T21:45:52

120

Given this:

$5P_5=nPr="n!"/"n−r!"$

Replacing...

$"5!"/"5−5!"$

Cancel out...

$5⋅4⋅3⋅2⋅1$

$20⋅3⋅2⋅1$

$60⋅2⋅1$

$120$