Thread: Calculating number of non consecutive numbers

Hi,

Can someone help me with a formula that will give me the number of non consecutive numbers in a given number of events.

So, if I had thirty selections how can I work out how many combinations of three numbers there are in the thirty selections. ie. 1,3,5 1,3,6 1,3,7 etc

I would like a formula that allows me to put in the total number of events coupled with the number of selections. So, I would like to be able to work out, say, the number of four non consecutive groups in a total of, say, ten selections.

As you've probably realised this is linked to some gambling probabilities. Hope you can help.

parkingticket60

I am not sure that I understand what you have written.
Here is a stab at an answer.
Consider the set of digits: .
I can select four of those with no two consecutive in ways.
We can select up to five digits with no consecutive digits.

If you had 15 items you can select up to 8 with no two consecutive.
For n items you can select up to with no two consecutive. That is the ceiling function.
The number of ways of selecting k items is .

If that is not what mean, please try to make is clear what you do mean.