Each of the elements in each set are different from one another. For example, A1 is different than A2. So also, the elements in set A are different than those in set B, e.g. A1 is different from B3. I am comfortable with the notion of n things taken r at a time, but I frankly never ran into a situation with a constraint such as - given that one may only choose 1 element from set A, etc. The answer you propose, 126, evokes a familiar but long neglected memory.
I very much appreciate your counsel. I have managed to maintain a love of mathematics, despite it remaining a foreign and ineluctable domain.
I am trying to define the number of unique combinations where: I have three mutually exclusive sets (A,B,C), each of which has a varying number of elements, viz.(A=6; B= 7; and C = 3), and the combinations must have three elements, with one and only one element from each of the three sets. I don't know why I am having difficulties with this, but, alas, I am. Any help would be very much appreciated.