How many ways can you arrange 7 students with specific groupings in a line?

[hari_299]

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I have a question here. Please can someone solve this. The question is:
There are 7 students of whom 2 are Americans, 2 are Russians and 3 Indians. hey have to stand in a line so that the two Americans are always together and the three Indians are always together. In how many ways can this be done??

 

[Muzza]

If there were only one American and one Indian, could you solve this problem?

 

[HallsofIvy]

In other words, treat the two Americans and the three Indians as being single persons. Once you know how many ways you can line up those "4 people", think about how many new ways you could get by interchanging the Americans only or interchanging the Indians only.