A batch of parts contains 80 parts from Batangas supplier of engine and 120 parts from as supplier of engine in Bulacan. If

five parts are selected randomly and without replacement, find the probability that (a) they are all from Batangas supplier;

(b) three or more parts in the sample are from Batangas; (c) at most two parts in the sample are from Batangas supplier;

and (d) at least one part in the sample is from Batangas supplier.