#### Peter Duncan

##### New member

- Joined
- Jan 11, 2018

- Messages
- 2

**Problem with combinations: Find fraction of total w/ more A’s than B’s**

Hi,

I would like to know which formula to use for the following combinations, please.

A or B can be chosen x times to generate a series of length x. A and B can be chosen as often as you like. Order does not matter. The question for each series is: For what fraction of the total are there more A’s than B’s?

Examples: If x=2, possibilities are A-A, A-B, B-A, B-B so how often are there more A’s than B’s? That is 1 out of 4=0.25.

If x=4, possibilities are A-A-A-A, A-A-A-B, A-A-B-A, A-A-B-B, A-B-A-A, A-B-A-B, A-B-B-A, A-B-B-B, B-A-A-A, B-A-A-B, B-A-B-A, B-A-B-B, B-B-A-A, B-B-A-B, B-B-B-A, B-B-B-B so how often are there more A’s than B’s? That is 5 out of 16=0.3125.

I can do these by hand, but it becomes more difficult when x=62.

Note that I am not giving any examples where x is an odd number, because that answer would always be 0.5.

A formula would be sooooo helpful!

Thank you, Peter