By using this formula "nPr = n! / (n-r)!". create a real-life scenario using permutation without repetition

Let's create a real-life scenario using the concept of permutations without repetition:

### Scenario:
A teacher wants to select and assign **3 different class monitor roles** (leader, assistant leader, and coordinator) to 10 students in her class. The order in which the students are selected matters because each role is different.

To find the number of ways the teacher can assign these 3 roles from the 10 students, we can use the **permutation formula**:

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

Where:
- \( n = 10 \) (the total number of students)
- \( r = 3 \) (the number of roles or positions to fill)

Using the formula:

\[
10P3 = \frac{10!}{(10 - 3)!} = \frac{10!}{7!}
\]

Since \( 10! = 10 \times 9 \times 8 \times 7! \), the \( 7! \) cancels out, so:

\[
10P3 = 10 \times 9 \times 8 = 720
\]

Thus, there are **720 different ways** to assign the 3 roles to the 10 students.

### Explanation:
- The permutation without repetition is used because once a student is assigned a role (leader, assistant leader, or coordinator), they cannot be assigned another role.
- The order of the assignment matters because each role is distinct (leader, assistant leader, coordinator).

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Do you need any further details or clarifications?

Here are 5 questions related to this scenario:
1. What happens to the calculation if we increase the number of students to 12?
2. How would the formula change if the teacher had to assign 4 roles instead of 3?
3. How does the situation change if the order of the roles doesn't matter?
4. What is the difference between permutations and combinations in such scenarios?
5. How can we apply this to a scenario where the roles can be filled by the same student?

**Tip:** Always remember that in permutations, the order matters, unlike combinations!

By using this formula 'nPr = n! / (n-r)!'. create a real-life scenario using permutation without repetition.

Explore a real-life scenario of using permutations without repetition to assign 3 roles (leader, assistant, and coordinator) to 10 students. Learn how to apply the permutation formula nPr = n! / (n-r)! to find there are 720 ways to assign these roles. This concept is key in combinatorics and is suitable for Grades 9-12.

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