How many possibilities are there for the win, place, and show (first, second, and third) positions in a horse race with 12 horses if all orders of finish are possible? There are ? different ways.
In a race with twelve horses, there are three prizes. Find the following:
A. How many possibilities are there for the win, place, and show (first, second, and third) positions in a horse race with 12 horses if all orders of finish are possible?
There are ? different ways.
B. Suppose some nefarious individual lames three of the twelve horses ensuring that they won't be among the top finishers. How many possibilities are there for the win, place, and show (first, second, and third) positions in a horse race to happen now?
There are ? different ways.
C. Suppose the three top prizes are all equal in value assigned to the top three finishers. How many possibilities are there for the prizes in a horse race with 12 horses if all orders of finish are possible?
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