Ten people run a race. There are no ties. (a) How many different orderings are there for how the participants finish the race? (b) How many orderings have Amy finishing immediately after Bai? (c) How many orderings don't have Eric finishing in first place or in second place or in third place? (d) First place gets a gold medal, second place gets a silver medal, and third place gets a bronze medal. Determine the number of ways the medals can be awarded to the participants