# Math Question: How Much To Bet A $1 Box/Wheel On Every Superfecta Combination With 20 Horses?

**URL:** <https://boards.straightdope.com/t/math-question-how-much-to-bet-a-1-box-wheel-on-every-superfecta-combination-with-20-horses/813593>\
**Category:** Factual Questions\
**Created:** [May 4, 2018, 6:22pm UTC](https://boards.straightdope.com/t/math-question-how-much-to-bet-a-1-box-wheel-on-every-superfecta-combination-with-20-horses/813593 "2018-05-04T18:22:05Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![HeyHomie](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/heyhomie/32/207_2.png) [@HeyHomie](https://boards.straightdope.com/u/HeyHomie)\
**Post date:** [May 4, 2018, 6:22pm UTC](https://boards.straightdope.com/t/math-question-how-much-to-bet-a-1-box-wheel-on-every-superfecta-combination-with-20-horses/813593/1 "2018-05-04T18:22:05Z")

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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?

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**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\
**Post date:** [May 4, 2018, 6:33pm UTC](https://boards.straightdope.com/t/math-question-how-much-to-bet-a-1-box-wheel-on-every-superfecta-combination-with-20-horses/813593/2 "2018-05-04T18:33:32Z")

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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](https://www.mathsisfun.com/combinatorics/combinations-permutations.html), 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.

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**Author:** ![don\_t\_ask](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)\
**Post date:** [May 4, 2018, 7:53pm UTC](https://boards.straightdope.com/t/math-question-how-much-to-bet-a-1-box-wheel-on-every-superfecta-combination-with-20-horses/813593/3 "2018-05-04T19:53:02Z")

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You can cut it down to $5,814 by only taking Mendelssohn to win.