Autonomous delivery pods are becoming an increasingly common way for commercial goods to be transferred or delivered from one party to another. Suppose n distinct autonomous model carry up to one each of k different standard delivery items. Furthermore, assume there are d different starting points and ending points per delivery route, delivery is direct, and no delivery starts and stops at the same point.

(a) How many distinct delivery configurations (each one having a different autonomous model, routes and sets of delivered items) exist with n=4, k=3, and d=4.

(b) Find a general formula for distinct configurations based on n, k, and d.

(c) Repeat (b) but assume half of the n models are unsuitable for delivery, one-quarter are suited to deliver half of the k items, and the last quarter are suited to deliver the other half.