I can’t do the math here. Let’s say (hypothetically) that I wanted to bet $1 on every possible Superfecta combination for Saturday’s Kentucky Derby. There are 20 horses running (as of the last time I looked). What would the total bet be?
I had to look up what a “superfecta” was: “in order to win, must pick the first four finishers of a race in the correct sequence.”
The number of different ways to select 4 horses out of 20 in sequence is a permutation, commonly written [sub]20[/sub]P[sub]4[/sub] or P(20,4).
The answer is 116,280 (so, at $1 each, that’s $116,280). This can be calculated as 20×19×18×17. There are 20 possibilities for which horse comes in first, each of which could be accompanied by any of the 19 other horses in second place, and etc.
You can cut it down to $5,814 by only taking Mendelssohn to win.