Answer :

Final answer:

In a race with 6 runners where there are no ties, the total number of possible outcomes is determined by calculating the permutation of these 6 runners. This translates to 720 possible ways the race could end.

Explanation:

For a race with 6 runners where there are no ties, the possible number of outcomes, or ways the race could finish, is determined by calculating the permutation of these 6 runners. In mathematics, a permutation is the number of different possible arrangements of a set of items. Here, the 6 runners can take any of the 6 places in the race. For the first place, there are 6 potential runners; for the second place, there are 5 remaining runners; for the third place, there are 4, and so on – until the last finishing place where there is only one runner left with one place to take. In mathematics, such situations are often dealt with the factorial function, which in this case, is 6! (6 factorial). Therefore, the total number of different ways the race could end is 6 x 5 x 4 x 3 x 2 x 1 = 720.

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