Maths on 4 horse combination tricasts?

colin300

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!

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.

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.

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.

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?