Find the value of each expression. Show your work.18.) ₉P₃

We have to find the value of 9P3 which means the Permutations of 9 objects taken 3 at a time.

The formula of permutations is:

[tex]nPr = \frac{n!}{(n-r)!} [/tex]

In the given case n=9 and r=3. Using these values, we get:

[tex]9P3= \frac{9!}{(9-3)!} \\ \\ = \frac{9!}{6!} \\ \\ = \frac{9*8*7*6!}{6!} \\ \\ =9*8*7 \\ \\ =504 [/tex]

Thus 9P3 is equal to 504.

9! is expanded above using the following  factorial formula:

n! = n(n-1)(n-2)(n-3)....3.2.1