The expression $7P5$ represents the number of permutations of 7 items taken 5 at a time.

The formula for permutations is given by:

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

Where:

• $n$ is the total number of items,
• $r$ is the number of items to choose.

For $7P5$:

$7P5 = \frac{7!}{(7 - 5)!} = \frac{7!}{2!}$

Now, let's calculate it step by step.

Step 1: Calculate the factorial of 7 ($7!$):

$7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040$

Step 2: Calculate the factorial of 2 ($2!$):

$2! = 2 \times 1 = 2$

Step 3: Divide $7!$ by $2!$:

$7P5 = \frac{5040}{2} = 2520$

Final Answer:

The value of $7P5$ is 2520.

Would you like more details or have any questions?

Here are some related questions:

1. What is the difference between permutations and combinations?
2. How do you calculate combinations $nC r$?
3. Can you explain the factorial function and its applications?
4. What are real-life examples of permutations?
5. How do you calculate permutations with repetition allowed?

Tip: Permutations are used when the order of selection matters, such as in arranging objects in a specific sequence.