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Dustin, a competitive athlete, is figuring out which races to sign up for next year. There are many types of races to choose from, including 5K5\text{K} runs, century rides, and ultramarathons. If Dustin signs up to complete one of each type, in how many different orders could he complete them?\newline_____\_\_\_\_\_ orders

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Full solution

Q. Dustin, a competitive athlete, is figuring out which races to sign up for next year. There are many types of races to choose from, including 5K5\text{K} runs, century rides, and ultramarathons. If Dustin signs up to complete one of each type, in how many different orders could he complete them?\newline_____\_\_\_\_\_ orders
  1. Events List: List of events: 55K run, century ride, and ultramarathon.\newlineDustin wants to complete one of each type of race.\newlineNumber of events: 33\newlineNumber of orders: 3!3!
  2. Factorial Calculation: Find the value of 3!3!.
    Number of orders = 3!3!
    = 3×2×13 \times 2 \times 1
    = 66

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