# Thread: Calculating Possibilities and Combinations

1. ## Calculating Possibilities and Combinations

Hi everyone,

I have a situation which I need help calculating.

I have 15 selections to choose from and each selection has a 50/50 ratio of being correct. I want to figure out how many combinations I can choose for each selection in order to cover all possibilities. On each of the 15 selections, one number must be chosen. For example, for the first selection, I must select 1 or 2. For the second I must select 3 or 4, etc.

Example:

1 - 2
3 - 4
5 - 6
7 - 8
9 - 10
11 - 12
13 - 14
15 - 16
17 - 18
19 - 20
21 - 22
23 - 24
25 - 26
27 - 28
29 - 30

So one total combination is: 1-3-5-7-9-11-13-15-17-19-21-23-25-27-29. Another combination would be: 2-4-6-8-10-12-14-16-18-20-22-24-26-28-30. Another would be 1-4-6-8-10-11-14-16-17-20-21-24-26-27-30. The list goes on...so that's 3 different possibilities I just listed. Now, what I'm looking for is the total number of all combination to cover all possibilities when selecting.

Anyone know how I can calculate this?

Thank You,
Dan

2. ## Re: Calculating Possibilities and Combinations

every time you add another two-way choice, the number of possibilities doubles. so the answer is $\displaystyle 2^n$ where n is the number of times you are asked to choose between 2 options.

3. ## Re: Calculating Possibilities and Combinations

Oh ok, didn't realize it was that simple...thanks a lot