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1. The number of different batting orders are possible using the starting lineup is 3628800

   How to determine the number of different batting orders are possible using the starting lineup?

   The given parameter is

   Players, n = 10

   The different batting orders are possible using the starting lineup is calculated using the following permutation expression

   Ways = nCn

   Substitute the known values in the above equation

   Ways = 10P10

   Apply the permutation formula

   Ways = 10!/(10 – 10)!

   Evaluate the difference

   Ways = 10!/0!

   0! = 1

   So, we have:

   Ways = 10!/1

   Evaluate

   Ways = 10!

   Expand

   Ways = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

   Evaluate the product

   Ways = 3628800

   Hence, the number of different batting orders are possible using the starting lineup is 3628800

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