find the number of batting orders for nine baseball players when the best two batters must be in the second and third positions

Question

anonymous · Answer

The easiest way to do this is to draw 9 lines and list your options
9 1 1 6 5 4 3 2 1
_ _ _ _ _ _ _ _ _

So we have 9*6*5*4*3*2 different lineups

anonymous · Answer

yeah i know that but isnt there a easier way with the permutation equation?

anonymous · Answer

this other website says        9! - ( 8! * 2 ! )     and the answer is right

phi · Answer

There are 9 batters.  However, 2 are pre-selected.   that leaves  7 batters and 7 slots.
there are 7! ways of assigning the 7 batters to the 7 slots.

anonymous · Answer

can you explain this?:         9! - ( 8! * 2 ! )

anonymous · Answer

Ah sorry the first should be a 7 not 9 since the 1 and 1 are already preselected as phi says