sampling based upon probability of event occurrence

I have a sampling and probability question.

A sub-assembly is assembled from 2 parts, A and B. Both are molded parts that are molded with 8-cavity molds. When a lot of either is made, the lot is comprised of equal parts from each of the 8 cavities. For A and B, 20,000 parts are made of each and each bin of parts is a mixture from all 8 cavities. To make the sub-assembly, an operator will randomly select from the bin of 20k for part A and the bin of 20k for part B. How many parts need to be made in order to have a high probability that one of each of the 64 combinations is included?