[DISCRETE MATH] Need my work checked before submission

[oblique isle]

Hey all! I was just hoping someone could check my work before I submitted my assignment.

[upper stump]

I think there might be some double counting. Let's say you have a division of 0's like this: 00|0|000 and another one like this: 0|00|000 with the same -arbitrary- four runs of 1's. Because you are counting all permutations of each division, one permutation of the first will lead to the second, so they have the same result