If 4 American, 2 French, and 3 British people are to be seated in a row, how many seating arrangements are possible when people of the same nationality must sit next to each other?
The Attempt at a Solution
If I "glue" the people together like so: ABF then there are 3! ways to arrange them. There are 4! ways to arrange the Americans, 2! to arrange the French, and 3! ways to arrange the british. Is the answer 3!4!2!3!= 1728?