# Math Help - How many bets are there?

1. ## How many bets are there?

I am trying to work out how many treble bets there are for any given number of selections, and for the life of me I can't. A treble consists of 3 different selections in 3 different events. Ie horse a in race 1 horse b in race 2 and horse c in race 3 combine to make the treble abc. I know that if I choose 4 horses in 4 races I have 4 trebles, 5 horses in 5 races equals 10 trebles and 6 equals 20 trebles. But what I need to calculate is the effect of 1 or more non runners. Each treble that has a non runner in it becomes a double ie a,b,nr or a,nr,b becomes a double. A bet with 2 nr in it becomes a single and a bet with 3 nr in it becomes void. For instance 5 selections equals 10 trebles. If 1 of those 5 is a nr then the 10 trebles become 4 trebles and 6 doubles. If there are 2 nr then the 10 trebles become 1 treble 7 doubles and 3 singles and so depending on the number of nr. Can anyone provide a formula please that will calculate the number of trebles doubles singles and voids given N number of selections and X number of nr's.

Many thanks for all and any help.

2. ## Re: How many bets are there?

Hey siala.

For the treble, you might want consider NC3 where N is the number of horses in the race. NC3 finds the number of ways of picking 3 horses from the total of N horses.

Easy Permutations and Combinations | BetterExplained

3. ## Re: How many bets are there?

Chiro thanks for your reply and the link, but I am making no headway. The frustrating thing is is that I can see the pattern, as shown in the table below, but I am no nearer in figuring out how that pattern is arrived at. If anyone can help I'd be most grateful. Thanks.

Code:
sel	nr	treble	      double	      single	     void
4	0	4		0		0		0
1	1		3		0		0
2	0		2		2		0
3	0		0		1		3
4	0		0		0		4

5	0	10		0		0		0
1	4		6		0		0
2	1		6		3		0
3	0		3		6		1
4	0		0		6		4
5	0		0		0		10

6	0	20		0		0		0
1	10		10		0		0
2	4		12		4		0
3	1		9		9		1
4	0		4		12		4
5	0		0		10		10
6	0		0		0		20