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Maths on 4 horse combination tricasts?

  • 01-08-2006 8:24pm
    #1
    colin300
    Closed Accounts Posts: 441 ✭✭


    Right I work in a bookies and the thing I can't seem to find out is this not even the customers who bet it dont know how it comes about.

    A customer puts 4 horses down on for a tricast and somehow it adds up to 24 tricasts obviously a combination but how is that possible i have messed around with the maths of it but I can't come to a conclusion. I would be interested if someone could explain the whole way it comes about.


    Thanks in advance!


Comments

  • #2
    frodi
    Registered Users, Registered Users 2 Posts: 520 ✭✭✭frodi


    Lets call the horses A, B, C, D.
    For all the below it's 1st, 2nd, 3rd


    1 A B C
    2 A B D
    3 A C B
    4 A C D
    5 A D B
    6 A D C
    7 B A C
    8 B A D
    9 B C A
    10 B C D
    11 B D A
    12 B D C
    13 C A B
    14 C A D
    15 C B A
    16 C B D
    17 C D A
    18 C D B
    19 D A B
    20 D A C
    21 D B A
    22 D B C
    23 D C A
    24 D C B

    The maths is 4 x 3 x 2 = 24
    Four choices with 3 picks.


  • #3
    colin300
    Closed Accounts Posts: 441 ✭✭colin300


    well dont i look like the idiot after looking at that its so simple i was looking at it in such a more difficult way. Like the way u calculate how many doubles are in 4 selections and so on.

    Cheers.


  • #4
    Crumbs
    Registered Users, Registered Users 2 Posts: 1,080 ✭✭✭Crumbs


    colin300 wrote:
    well dont i look like the idiot after looking at that its so simple i was looking at it in such a more difficult way. Like the way u calculate how many doubles are in 4 selections and so on.
    Calculating things like doubles from 4 selections etc. is to do with "combinations" and calculating things like tricasts from 4 selections is "permutations". Unfortunately, the two words seem to be thought of as interchangeable by a lot of people but they mean different things.


  • #5
    Robin1982
    Closed Accounts Posts: 323 ✭✭Robin1982


    Permutation - order matters
    Combination - order doesn't matter

    Bookmakers Tricast - bet to predict the first three finishers in the correct order

    # of selections (n): 4
    # of results (r): 3

    Permutation: (n!)/(n-r)! => (4!)/(4-3)! = (4x3x2x1)/(1) = 24 ways

    Tote Trio - bet to predict the first three finishers in any order

    # of selections (n): 4
    # of results (r): 3

    Combination: (n!)/(r!)(n-r)! => (4!)/(3!)(4-3)! = (4x3x2x1)/((3x2x1)(1)) => 24/6 = 4 ways

    Same formulas can be used for doubles and/or any number of selections/results.

    Once you understand the above, more interesting bets can be constructed i.e. :

    Mythical Sussex Stakes Tricast:

    Strong Win Fancies: Echo Of Light, Araafa
    Place Fancies: Court Masterpiece, Aussie Rules, Soviet Song

    How could you construct your tricast bets to reflect you fancies and how many bets (ways) would it be?


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