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Question 15, 11.2.45
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In a race in which six automobiles are entered and there are no ties, in how many ways can the first three finishers
come in?
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Answer 1

Hello! I'm here to help you with your question. To answer your question, we need to use combinatorial mathematics. In a race with six automobiles and no ties, the first three finishers can come in $6 \times 5 \times 4 = 120$ different ways.

Here's the calculation:

1. The first car can finish in any of the six positions (1st, 2nd, 3rd, ..., 6th). There are 6 choices for the first car.

2. The second car can finish in any of the remaining positions (4th, 5th, 6th). There are 6 choices for the second car.

3. The third car can finish in any of the remaining positions (5th, 6th). There are 3 choices for the third car.

Therefore, the total number of ways the first three finishers can come in is:

6 x 6 x 3 = 120

So, there are 120 different ways the first three finishers can come in.

Explanation: