PMac outlined it perfectly... and unfortunately it would still cost a pretty good amount to cover well. Lets say hypothetically you need to use 5 in each of the first and last legs, and if the key speed horse doesnt win there's 3 other contenders in the middle legs. Your ticket would then cost 5X5X3X3X1X1 = 225 combinations or $450, times 6 tickets for each of the double single combinations = $2700.
I think your idea is excellent but in practice still very difficult and the reason the pick 6 is such a tough wager.
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