Question

Find the value of each expression. Show your work.

18.) ₉P₃

Answer 1

The value of the expression is 504.

Explanation:

We are given the expression
`9P3`.

Now,
`9P3` represents the permutations of 9 objects which are taken 3 at a time.

Also, its value is given by,

`9P3=(9!)/((9-3)!)\\\\9P3=(9!)/(6!)`,

where ! represents the factorial given by,

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

Thus, evaluating the expression, we get,

`9P3=(9!)/(6!)\\\\9P3=(9* 8* 7* 6!)/(6!)\\\\9P3=9* 8* 7\\\\9P3=504`

Thus, the value of the expression is 504.

Answer 2

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:


`nPr = (n!)/((n-r)!)`

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


`9P3= (9!)/((9-3)!) \\ \\ = (9!)/(6!) \\ \\ = (9*8*7*6!)/(6!) \\ \\ =9*8*7 \\ \\ =504`

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