Question

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

Explanation:

Step1: Identify the problem type

This is a permutation problem because the order of the finishers matters (first, second, third are distinct positions). The formula for permutations of \(n\) objects taken \(r\) at a time is \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n = 5\) (total automobiles) and \(r=3\) (positions to fill: first, second, third).

Step2: Apply the permutation formula

Substitute \(n = 5\) and \(r = 3\) into the formula:

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Answer:

60