In how many ways can we form an international commission if we must choose one European country from among 6 European countries, one Asian country from among 4, one North American country from among 3, and one African country from among 7?
I need to count the number of possible combinations of one country from each region. I can use the multiplication principle, which says that if I have a choice of a things and then a choice of b things, regardless of what I choose first, I have a total of a times b choices. In this case, I have a choice of 6 European countries, then 4 Asian countries, then 3 North American countries, and then 7 African countries. So, by the multiplication principle, I have 6 times 4 times 3 times 7 choices, which is 504. 