Question 230503
How many batting lineups are there for the nine players of
a baseball team if the center fielder must bat fourth and the
pitcher last?
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Since center fielder and pitcher are already assigned only
7 positions need to be filled with the seven remaining 
players.
7 ways to assign the 1st
6 ways to assign the 2nd
5 ways to assign the 3rd
etc.

7! = 7*6*5*4*3*2*1 = 5040
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Cheers,
Stan H.