In how many different orders can five runners finish a race if no ties are allowed?

Since there are a total of 5 runners, there are 5 possibilities for 1st place. The possibilities for 2nd place are 4 since there are only 4 runners left. For the 3rd, there are possibilities of 3 runners. For the 4th place, there are 2 possibilities and 1 remaining possibility for the 5th place. Multiplying all the possibilities will give you the total number of different orders that 5 runners can finish the race.

Total number of different orders = 5 * 4 *3 * 2 * 1 = 120

You can confirm this using tree diagram.

rational decision making is a multi-step process for making choices between alternatives. the process of rational decision making favors logic, objectivity, and analysis over subjectivity and insight. the word “rational” in this context does not mean sane or clear-headed as it does in the colloquial sense.

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