Identify the following as Permutations, or Combinations (no need to solve). In a race in which six automobiles are entered and there are not ties, in how many ways can the first four finishers come in?

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BlackTom AI · Accepted Answer

The question asks us to identify whether the scenario corresponds to a permutation or a combination. 
Option a: Combination. This would be appropriate if the order of the four finishers did not matter, i.e., only which four cars are in the top four mattered. However, in a race, the order of finish is important because first, second, third, and fourth place are distinct positions. Therefore, treating this as a combination would ignore the critical element of order.
Option b: Permutation. Since the finish order matters (who finishes first, who finishes second, etc.), the arrangement of the four cars matters. This aligns with the definition of a permutation, where the sequence or order of selected items is significant.
In summary, the scenario emphasizes the importance of order (first through fourth), which is characteristic of a permutation rather than a combination. Therefore, the correct category for this situation is permutation.

MDM4U - Mathematics of Data Management 12 (2025-26) - A

Identify the following as Permutations, or Combinations (no need to solve). In a race in which six automobiles are entered and there are not ties, in how many ways can the first four finishers come in?

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