I am looking for an equation to predict the resulting number of sets from a Cartesian products of N sets, with varying length. The sets look similar to as follows (but there are about 60 of them):
A=[a1, a2, a3, a4], B=[b1, b2, b3, b4, b5], C=[c1, c2], D=[d1, d2, d3, d4], E=[e1, e2]
Each product will have one element from each set (eg. [a2, b2, c2, d3, e1]) and their order does not matter (elements from a through e will remain in the same position of each set).
Any suggestions?