Your terminology is a little ambiguous but for the obvious interpretation your answer is mostly correct.
If you really mean you want to pick one item from each list, and keep the resulting 4-tuple in the order of [item from list 1, then from list 2, then from list 3, then from list 4] then yes, there are count1 * count2 * count3 * count4 such tuples.
If list 1 has 2 values the same, then two of those resulting tuples will appear to be identical. e.g. if items a and j in list 1 are the same value then tuples (listitem1-a, listitem2-b, listitem3-c, listitem4-d) and (listitem1-j, listitem2-b, listitem3-c, listitem4-d)
will appear identical.
If list 1 and list 2 both have a value in common that occurs only once in each list, then the good tuple (listitem1-a, listitem2-b, listitem3-c, listitem4-d) will look the same as the defective tuple (listitem2-b, listitem1-a, listitem3-c, listitem4-d)
Whether you care or not about those identical looking tuples is up to you.