How do you evaluate 5P5?

Question

47791 views around the world

You can reuse this answer
Creative Commons License

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#