If 4 Americans, 3 Frenchman, and 3 Englishmen 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?

4 Americans can arrange themselves in 4! ways. similarly, 3 Frenchmen can arrange themselves in 3! ways. 3 Englishmen can arrange themselves in 3! ways. now these 3 groups of same nationality people can be arranged among themselves in 3! ways. so total number of ways = 3!4!3!3!