How many different ways can a 1st 2nd and 3rd place winner finish a race if there are 6 runners?

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Backing a horse to win or place is as simple - and for many, as good! - as punting gets. Of all the bet types available these are the two most simple to place; they are also the easiest to follow and enjoy as a punter. All you need to do is keep an eye on your selection in running and hope they manage to win or place, in keeping with your bet.

Punters can also back a horse to Win AND Place, this is better known as an Each Way bet.

A Win bet is a bet type that requires the punter to select the horse they believe will be first past the post. If they are correct they will win a sum of money relevant to their investment and the betting product (Fixed Odds or Tote betting). A Place bet is a bet type that requires you to select a horse that finishes in the placings, meaning either 1st, 2nd or 3rd*. * The number of runners in the field will determine the amount of placings that will be paid out. - For fields of seven or fewer runners, the place dividend is only paid out across 1st and 2nd.- For fields of four or fewer runners, there will be no place dividend paid out.If you have already put on a Place bet and then a scratching reduces the field size to seven or fewer, your bet will be subject to the rules applying to the reduced field size. If you have a Place bet on a race with five runners and a scratching(s) reduces the field to four (or fewer), your bet will then be refunded, subject to the rules of each bookmaker and the betting product (Tote or Fixed Odds) selected. The cost of a Win / Place bet is $1 for one full unit, i.e. 100% of the relevant dividend. A punter can take as many units as they like, subject to the gambling agency being prepared to take on liability for the bet. The more units a punter takes, the more the bet will cost them. So for five units a punter would be required to outlay $5. If you place a $5 Win bet on a horse you will receive 500% of whatever betting product - i.e. Tote or Fixed Odds - selected for the wager. Some wagering operators have minimum bets of $1 while others will allow even smaller wagers. Consult individual operators' wagering rules and restrictions for more on this. When wagering on a Win or Place bet, punters may have the choice of Fixed Odds or Tote Betting (including any bookmaker's individual tote product). After selecting your horse, choosing between the tote price and fixed odds is probably the next hardest decision a punter will have to make. The tote price is determined by a betting pool containing the spread of individual bets placed on a particular event. The horse that has attracted the most amount of money will be paying the least, while the horse that has attracted the least amount of money will be paying the highest. The actual tote dividend is only revealed after the race and can often change quite significantly in the lead-up to the race. The closer they are to jumping, the more likely the tote price will reflect the eventual dividend. Fixed odds allow punters to secure a set price on a runner in a given event. Fixed odds can help astute punters lock in value on a runner they suspect is over the odds and is likely to be the subject of significant support among other punters by the close of betting. There is no prescriptive guide or right answer to the question of Tote betting vs fixed odds: the success of either generally depends on your astuteness - and luck - as a punter. Generally speaking though Fixed Odds are at their best when markets first open. And if you get involved with online betting you can compare bookmakers to find the most competitive price out there.
Watching your horse storm home over the top of its rivals - or hold off all challengers in gritty fashion - can be one of life's great joys. Take this gentleman's celebration, for example;

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Kyden L.

asked • 04/10/20

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1 Expert Answer

Abigail H. answered • 04/10/20

PA Certified 7-12 Math Tutor

Assuming that there cannot be a tie, here is how you can approach this problem.

There are five runners, so there are five different possibilities of who can come in first place.

Now, once someone comes in first place, there are only 4 runners left who can come in second place.

Likewise, there are only 3 runners left who can come in third place.

You want to then multiply 5*4*3 to represent the different combinations we can make for each place.

This gives us a total of 60 different possible ways that the runners can come in 1st, 2nd, and 3rd place, assuming no ties.

    Let's look at two problems that involve factorials.

Problem 1:

    If there are 8 different books on a shelf, how many ways are there to arrange those books?

    Imagine placing all the books on the floor. One would have to choose between 8 different books to be placed first on the shelf. Once picked, there would be 7 books remaining that could also be picked for the second place on the shelf. Once that book is placed on a shelf, there would be 6 books to choose from, and so on.

    Using the fundamental counting principal, the math would look like this.

    There are 40,320 ways to arrange these 8 books.

Problem 2:

    If there are 4 people who need to be seated at a circular table, how many different ways can this be done?

    It appears this problem is the same as problem #1 above but it has less objects to arrange. We could list all the possibilities. We will list the people as person A, person B, person C, and person D.

    The problem with this list, which lists all combinations of A, B, C, and D, it does not take in to consideration that there is a circular table. However, it is a great list for placing people in a line.

    The difference is, there are situations listed there that are the same. Here are arrangements that are exactly the same, because of the circular situation.

    Take any letter. Look to its left and right and you will see identical adjacent letters in each set. This means the only true unique situations we can gain is by looking down one of the columns from our large 24-set list above. So, there really are only 6 unique arrangements.

    This means if we take one less than our number of people, we can simply use factorials.

    There are 6 ways to arrange 4 people at a circular table.

    Note: This means if we started with 8 people, we could calculate the total possible ways to arrange them around a table by calculating 7!, which is 5,040.