Re: Number of combinations

Quote:

Originally Posted by

**billobillo** If I have numbers from 1 to N and I want to select K out of them.

In how many ways I can select these K numbers such that they contain at least two consecutive numbers.

For example if N=7 and K=3, I want to select combinations such as {1,2,3) , {2,3,7} , {3,5,6} but not {1,3,5} or {2,4,7} ....

First note that if , that is the ceiling function, there are of pick a subset of numbers with __no__ consecutive numbers. So subtract from the total.

If then any subset of numbers with **must contain consecutive numbers.**

I do not understand the second part at all.

Re: Number of combinations

Quote:

Originally Posted by

**Plato** First note that if

, that is the ceiling function, there are

of pick a subset of

numbers with

__no__ consecutive numbers. So subtract from the total.

If

then any subset of

numbers with

**must contain consecutive numbers.**
I do not understand the second part at all.

Thank you for the reply, I guess you are the genius of this forum :), in first part the difference between any 2 of the K numbers should be >= "1"; you answer is correct.

In the second part , I need to choose a number other than "1" i.e. if D="2" , then the difference between any 2 of the K numbers should be >= "2"

For example : If D=2, I need set like {1,3,5} where 3-1>=2 and 5-3>=2 and 5-1>=2 OR set like {2,4,7} ......

Or If D=3 I need number of sets like {1,4,7} where 4-1>=3 and 7-4>=3 and 7-1>=3.

Is there a way to create a general formula that takes N,K and D and give me the number of combinations allowed?

Regards.