MHB How many ways can the captain arrage her schedule?

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Captain Jane Way has a total of ten destinations to choose from for her charter plane trips. The number of ways she can arrange her schedule is calculated by finding the factorial of the number of destinations, which is 10!. For the first destination, she has ten choices available. Each subsequent choice decreases by one as destinations are selected. The total arrangements highlight the complexity and variety in scheduling for charter flights.
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Captain Jane Way is a charter plane pilot and has trips scheduled to Seattle,Dallas, San Francisco, New York, Portland, Omaha, Miami, Honolulu, Arlington, Los Angeles, and Chicago. How many ways can the captain arrage her schedule?
 
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How many choices does the good Captain have for the first destination on her schedule?
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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