Consider throwing m balls into n bins, and for convenience let the bins be numbered from 0 to n 1. We say there is a k-gap starting at bin i if bins i, i + 1, . . . , i + k 1 are all empty. (a) Determine the expected number of k-gaps. (b) Prove a Chernoff-like bound for the number of k-gaps. (Hint: If you let Xi = 1 when there is a k-gap starting at bin i, then there are dependencies between Xi and Xi+1; to avoid these dependencies, you might consider Xi and Xi+k.)