1. ## Possible Combinations Question. Please Assist.

Hello all,

I have been hoping to solve a problem involving all possible combinations for a set of integers. I started scribbling combinations out on paper, but I thought there might be some type of equation that could tell me the maximum possible combinations given a certain scenario. In addition to that I was hoping to map out all the combinations individually provided the number of combinations isn't much more than 30 or so.

Ok, here is the given information. Given 20 integers from the range 0-19, I need to pull 10 integers from that set. They must not repeat, and will be listed in ascending order. Also, there must be 5 integers selected from the range 0-8, 3 integers from 9-14, and 2 integers from 15-19 in this set. Given this information, how many possible combinations are there, and what are they?

(I have written out 8 this far, but I'm sure there are more...)

Thanks in advance for any assistance.

2. ## Re: Possible Combinations Question. Please Assist.

Originally Posted by crazed
Given 20 integers from the range 0-19, I need to pull 10 integers from that set. They must not repeat, and will be listed in ascending order. Also, there must be 5 integers selected from the range 0-8, 3 integers from 9-14, and 2 integers from 15-19 in this set. Given this information, how many possible combinations are there, and what are they?

Any subset of ten integers can be arranged in ascending order.

How many subsets of five from $\displaystyle \{0,~1,\cdots 8\}$ are possible?

How many subsets of three from $\displaystyle \{9,~10,\cdots 14\}$ are possible?

How many subsets of two from $\displaystyle \{15,~16,\cdots 19\}$ are possible?

Now multiply.