There are six students of whom 2 are Indians, 2 Americans and the remaining 2 are Russians. They have to stand in a line so that the two Indians are together, the two Americans are together and so also the two Russians. Show that there are 48 different ways of arranging the students.

Solution

Consider 2 Indian as 1 unit, 2 Americans as 1 unit and 2 Russians as 1 unit. Now there are 3 units and they can be arranged among themselves in 3! ways. In each of such arrangements the 2 Indians can be arranged among themselves in 2! ways, the 2 Americans can be arranged among themselves in 2! ways and the 2 Russians can be arranged among themselves in 2! ways.

∴ Total number of arrangement are as 3! x 2! x 2! x 2! = 48 ways