We provide complete average-case as well as probabilistic analysis of the cost of bucket selection and sorting algorithms. Two variations of bucketing (and flavors there in) are considered: distributive bucketing (large number of buckets) and radix bucketing (recursive with a small number of buckets, suitable for digital computation). For Distributive Selection a compound Poisson limit is established. For all other flavors of bucket selection and sorting, central limit theorems underlying the cost are derived by asymptotic techniques involving perturbation of Rice's integral and contour integration (saddle point methods). In the case of radix bucketing, periodic luctuations appear in the moments of both the selection and sorting algorithms.