Short Answer 
The permutation formula, ( n P r = n! / (n – r)! ), is used to calculate arrangements of ( r ) elements from ( n ). In this case, with ( n = 15 ) dishes and ( r = 3 ) to arrange, the total number of arrangements is calculated as 2730.
Step 1: Understand the Permutation Formula
The permutation formula helps calculate the number of arrangements of r elements from a total of n elements. The formula is represented as:
- n P r = P(n, r) = n! / (n – r)!
Knowing this formula allows you to determine the different ways objects can be arranged when the order matters.
Step 2: Identify the Variables
In this problem, we need to identify the values of n and r. Here, n represents the total number of dishes, and r represents the number of dishes to arrange:
- n = 15 (total number of dishes)
- r = 3 (number of dishes to arrange)
Understanding these values is crucial for applying the permutation formula correctly.
Step 3: Calculate the Number of Arrangements
Using the identified values in the permutation formula, we proceed with the calculation:
- Calculate P(15, 3) = 15! / (15 – 3)!
- This simplifies to 15! / 12! = 15 √ó 14 √ó 13
- Therefore, the total number of arrangements is 2730.
By following these steps, you can easily find the number of ways to arrange selected elements from a larger set.