Question 397991
If the top of the lineup is considered first, there are only
8 choices for 1st batter, then 7 choices, 6,  and 5
So the number of choices for the top 4 positions are
{{{8*7*6*5}}} then the pitcher becomes available  plus the
4 others left. {{{4 + 1 = 5}}}, next here are 4 choices, then 3,
2, and 1
{{{8*7*6*5*5*4*3*2*1 = 201600 }}}  is the sum of all the choices
Hope I got it right