How do you evaluate 5P5?

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Answer 1 · 2017-06-18T21:45:36

The simple answer is 120.

$_{5} P_{5}$ $"_5P_5$ 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 $_{n} P_{n}$ $"_nP_n$ is $n!$ $n!$ .

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

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

$_{n} P_{r} = \frac{n!}{(n - r)!}$ $"_nP_r = (n!)/((n-r)!)$

Answer 2 · 2017-06-18T21:45:52

120

Given this:

$5 P_{5} = n P r = \frac{n!}{n-r!}$ $5P_5=nPr="n!"/"n−r!"$

Replacing...

$\frac{5!}{5-5!}$ $"5!"/"5−5!"$

Cancel out...

$5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ $5⋅4⋅3⋅2⋅1$

$20 \cdot 3 \cdot 2 \cdot 1$ $20⋅3⋅2⋅1$

$60 \cdot 2 \cdot 1$ $60⋅2⋅1$

$120$ $120$