Problem

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?
There are ways for the first three finishers to come in.

Answer

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Answer

Final Answer: There are \(\boxed{60}\) ways for the first three finishers to come in.

Steps

Step 1 :This problem is about permutations. We have 5 automobiles and we want to know in how many ways we can arrange 3 of them. The formula for permutations is: \(P(n, r) = \frac{n!}{(n-r)!}\) where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.

Step 2 :In this case, n = 5 (the total number of automobiles) and r = 3 (the number of automobiles to finish the race).

Step 3 :Substituting the values into the formula, we get \(P(5, 3) = \frac{5!}{(5-3)!}\)

Step 4 :Solving the above expression, we get the permutation as 60.0

Step 5 :Final Answer: There are \(\boxed{60}\) ways for the first three finishers to come in.

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