Question

in a race in which seven automobiles are entered and there are no ties, in how many ways can the first three finishers come in?

the first three finishers can finish in \\(\square\\) ways.

Explanation:

Step1: Determine the number of choices for the first finisher

There are 7 automobiles, so there are 7 choices for the first - place finisher.

Step2: Determine the number of choices for the second finisher

After the first finisher is chosen, there are 6 automobiles left. So there are 6 choices for the second - place finisher.

Step3: Determine the number of choices for the third finisher

After the first two finishers are chosen, there are 5 automobiles left. So there are 5 choices for the third - place finisher.

Using the multiplication principle of counting (if one event can occur in \(m\) ways, and after that, another event can occur in \(n\) ways, and then a third event can occur in \(p\) ways, the total number of ways for the three events to occur in sequence is \(m\times n\times p\)), the number of ways the first three finishers can come in is \(7\times6\times5\).

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Answer:

210