Combinatorics/Permutation problem?

[ArcanaNoir]

Homework Statement

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?

Homework Equations

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?

 

[I like Serena]

I thought you had run away!

I'm starting to think that you like these problems!


(Oh, and yes, you have it right! )

 

[ArcanaNoir]

It's a miracle!

Oh, and I don't like these problems, I like passing my classes.