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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