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Q: Finite math question (\$3.00 Tip with answer) ( Answered ,   4 Comments ) Question
 Subject: Finite math question (\$3.00 Tip with answer) Category: Miscellaneous Asked by: egerbeaver-ga List Price: \$7.00 Posted: 27 Oct 2006 06:35 PDT Expires: 26 Nov 2006 05:35 PST Question ID: 777420
 ```I would like to bet on NHL games, but first I want to find out the odds. If there are 15 hockey games in one night, and you have to pick a winner from each game, what are the odds that you will get 1/15 games right, 2/15 games right,... 15/15 games right. I believe the total number of possibilities is 2 to the power of 15, but I can't figure out how many combinations there are for each. If you could reply in list form, that would be great. IE: 1/15 = 15/32,768 2/15 = x/32,768 ... 14/15 = x/32,768 15/15 = 1/32,768 Please explain how you got your answer. Thanks for your time.``` Subject: Re: Finite math question (\$3.00 Tip with answer) Answered By: justaskscott-ga on 27 Oct 2006 07:36 PDT Rated: ```Hi egerbeaver, Presuming an equal chance that you will win or lose each of your bets, the odds would be: 0/15 = 1/32768 1/15 = 15/32768 2/15 = 105/32768 3/15 = 455/32768 4/15 = 1365/32768 5/15 = 3003/32768 6/15 = 5005/32768 7/15 = 6435/32768 8/15 = 6435/32768 9/15 = 5005/32768 10/15 = 3003/32768 11/15 = 1365/32768 12/15 = 455/32768 13/15 = 105/32768 14/15 = 15/32768 15/15 = 1/32768 "The formula for finding the number of combinations of k objects you can choose from a set of n objects is: n! n_C_k = ---------- k!(n - k)! "Permutations and Combinations" The Math Forum @ Drexel http://mathforum.org/dr.math/faq/faq.comb.perm.html In essence, your question asks how many combinations of k objects you can choose from n objects (and what the ratio of that number of combinations is to the total number of combinations). There are 15 objects here -- the 15 hockey games. You "choose" 0 games if you win none of the bets; you "choose" 1 game if you win 1 bet; etc. There is only 1 way to choose 0 games -- by losing every bet. [ 15_C_0 = 15! / 0! * (15-0)! = 1 ] There is likewise only 1 way to choose 15 games -- by winning every bet. [ 15_C_15 = 15! / 15! * (15-15)! = 1] There are 15 ways to choose 1 game -- you could win only game 1, only game 2, and so on up to only game 15. [ 15_C_1 = 15! / 1! * (15-1)! = 15! / 14! = 15 ] There are likewise 15 ways to choose 14 games -- by losing only game 1, losing only game 2, and so on up to losing only game 15. [ 15_C_14 = 15! / 14! * (15-14)! = 15! / 14! = 15 ] You will find that the number of combinations for choosing 0, 1, and up to 15 games are arranged according to the 15th row of Pascal's Triangle. "Pascal's Triangle to Row 19" The Math Forum @ Drexel http://mathforum.org/dr.cgi/pascal.html "Pascal's Triangle" The Math Forum @ Drexel http://mathforum.org/dr.math/faq/faq.pascal.triangle.html The total number of combinations -- winning 0, 1, and up to 15 games -- is indeed 2 to the 15th power, or 32,768. This is equal to the numbers in the 15th row of Pascal's Triangle. The odds given above have the numbers from that row (i.e., the numbers calculated by the formula for n_C_k) as numerators, and the total number of combinations as the denominator. See also: "Introduction to Probability" The Math Forum @ Drexel http://mathforum.org/dr.math/faq/faq.prob.intro.html Please let me know if you need any clarification. - justaskscott Search strategy -- Searched on Google for: combinations permutations```
 egerbeaver-ga rated this answer: and gave an additional tip of: \$4.00 `Awesome! Exactly what I was looking for. Thank you very much.` Subject: Re: Finite math question (\$3.00 Tip with answer) From: myoarin-ga on 27 Oct 2006 12:54 PDT
 ```That is a great answer if you are just tipping blindly, but anyone following the league should be able to improve his chances by considering the realistic chances of top teams beating bottom teams.```
 Subject: Re: Finite math question (\$3.00 Tip with answer) From: barneca-ga on 28 Oct 2006 07:24 PDT
 ```i don't really follow hockey (heresy in the northeast u.s., so don't tell anyone), so i've never bet on it, but i assume like football or baseball, you have to either give odds, or bet on a point spread, so unless you know the league better than the market does, 50% odds are probably a reasonable guess. -cab```
 Subject: Re: Finite math question (\$3.00 Tip with answer) From: pofacedjo-ga on 28 Oct 2006 07:39 PDT
 ```I don't follow hockey either but is there not a chance of a draw. If so there are 3 possible outcomes.```
 Subject: Re: Finite math question (\$3.00 Tip with answer) From: egerbeaver-ga on 30 Oct 2006 15:58 PST
 ```Thanks for the comments. You are right that you can improve your chances by knowing which teams are better than others. I just wanted an approximation of how well I was doing. There was a girl who won \$444,000 on a \$5 bet by picking all 13 football games for the week right. I figured I would give it a shot. There are a few different ways to bet on hockey. You can bet on individual games (minimum 3) (win, lose, or tie), and you can bet whether the goal total will be over or under the average (5.5). On the weekends, they have have a pool where you pay \$5 and pick the winner out of 15 games. Who ever gets the most right, wins the pot. If multiple people get the same amount of games right, they share the pot. There are no ties in this game because if the game goes past overtime, they have a shootout to determine the winner.``` 