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

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Jayce Wintheiser

Feb 20, 2025

The number of orders that 5 runners can finish a race is 5! or 54321. The answer is 120.SInce there are 5 runners there are 5 possibilities for first place. The possibilities for second are 4 because there are 4 runners left to take second. That makes a total of 20 possibilities for first and second place winners. Third place will have 3 possible runners after first place and second have finished and fourth and fifth, four and five. That makes a total of 120 possibilities for first,second,third,fourth,and fifth place.You can confirm this with a tree diagram Hope this helped.... Show More
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