Evaluate the expression. $$ { }_{9} P_{5} $$ A. 15,120 B. 504 C. 1 D. 9

Question

UpStudy AI · Accepted Answer

To evaluate the expression $$ { }_{9} P_{5} $$, we use the formula for permutations, which is given by:

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

In this case, $$ n = 9 $$ and $$ r = 5 $$. Therefore, we can substitute these values into the formula:

$$
_{9}P_{5} = \frac{9!}{(9-5)!} = \frac{9!}{4!}
$$

Now, we can calculate $$ 9! $$ and $$ 4! $$:

$$
9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1
$$
$$
4! = 4 \times 3 \times 2 \times 1
$$

However, since we are dividing $$ 9! $$ by $$ 4! $$, we can simplify the calculation by canceling out $$ 4! $$ from $$ 9! $$:

$$
_{9}P_{5} = 9 \times 8 \times 7 \times 6 \times 5
$$

Now, let's calculate this step by step:

1. $$ 9 \times 8 = 72 $$
2. $$ 72 \times 7 = 504 $$
3. $$ 504 \times 6 = 3024 $$
4. $$ 3024 \times 5 = 15120 $$

Thus, we find that:

$$
_{9}P_{5} = 15120
$$

The correct answer is:

**A. 15,120**
The value of $$ { }_{9} P_{5} $$ is 15,120.

Evaluate the expression. \( { }_{9} P_{5} \) A. 15,120 B. 504 C. 1 D. 9