How do you evaluate 5P5?

Jun 18, 2017

Explanation:

"_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)!)

120

Explanation:

Given this:

$5 {P}_{5} = n P r = \text{n!"/"n−r!}$

Replacing...

$\text{5!"/"5−5!}$

Cancel out...

5⋅4⋅3⋅2⋅1

20⋅3⋅2⋅1

60⋅2⋅1

$120$