How many different orderings of 1st, 2nd, and 3rd place can there be among 7 runners in a race?

To determine the number of different orderings of 1st, 2nd, and 3rd place among 7 runners, we need to consider how many ways we can select and arrange those top three positions from the group of 7.

First, we select one runner for 1st place. There are 7 possible choices for this position. After selecting the 1st place runner, we have 6 runners left to choose from for 2nd place. Finally, for 3rd place, we have 5 runners left to choose from after selecting who came in 1st and 2nd.

The total number of different orderings can be calculated using the multiplication principle of counting:

• Number of choices for 1st place: 7

• Number of choices for 2nd place: 6

• Number of choices for 3rd place: 5

Now, we multiply these choices together to find the total number of possible orderings:

7 (choices for 1st) × 6 (choices for 2nd) × 5 (choices for 3rd) = 210.

Therefore, the total number of different orderings of 1st, 2nd, and