Assignment:
Suppose that there are a total of 19 students in an elementary school class. The teacher assigns each of the students a report on a mainland country in either North America or South America (not including the United States) and each student is assigned a different country. The North American countries that the teacher has to pick from are Belize, Canada, Costa Rica, El Salvador, Guatemala, Honduras, Mexico, Nicaragua, and Panama (for a total of 9 countries) and the South American countries they have to pick from are Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, French Guiana, Guyana, Paraguay, Peru, Suriname, Uruguay, and Venezuela (for a total of 13 countries).
Assuming that the order in which the countries are assigned doesn't matter:
a) In how many ways can the countries be assigned so that all of the North American countries are assigned?
b) In how many ways can the countries be assigned so that there is at least one North American that is not assigned and at least one South American country that is not assigned?
Provide complete and step by step solution for the question and show calculations and use formulas.