I have a number sequence from 1 to 100. Given 2 bins, the numbers are randomly assigned to each bin.
I know the total sum from 1 to 100 is 5050. Thus, for both bins to have the same sum, each bin must sum up to 2525. All the 100 numbers must belong to either bin.
I know there are a total of 2^100 possible combinations. How do I find the number of combinations that sum to 2525 in each bin?
EDIT: Just to clarify, a bin is just a collection of numbers. So essentially, I have collection A and collection B. The sum in each collection must be equal and all 100 numbers must belong to either collection. Think of them as buckets or whatever is convenient for explanation.