Final answer:
An example of a permutation without repetition is determining the order of runners finishing a race, and the formula is nPr = n! / (n - r)!, which calculates the number of permutations without repeating items.
Step-by-step explanation:
An example of a permutation without repetition would be selecting the order of runners in a race. Suppose you have 5 runners and you want to determine in how many different ways they could finish first, second, and third. There are 5 choices for first place, 4 choices for second place (since one runner already finished), and 3 choices for third place, making the total number of permutations 5 × 4 × 3.
The formula for permutations without repetition is nPr = n! / (n - r)!, where n is the total number of items and r is the number of items being chosen. In the runner example, n=5 and r=3, so the permutation would be calculated as 5P3 = 5! / (5 - 3)! = 5 × 4 × 3 = 60.