vipulgoyal wrote:hi Brent, In one more source I found the same qustion with 540 ans
6c2*4c2*3p3=540
does this require second thought??

The only way that 540 can be the answer is if we say that each team has a certain designation BEFORE they are assigned a topic.
For example, we might give names to the three teams: Lions, Tigers, Bears
This would mean that AB as the Lions team, CD as the Tigers team and DE as the Bears team is DIFFERENT from AB as the Tigers team, CD as the Lions team and DE as the Bears team.
In this case, we could assign the 6 people to the 3 teams in 90 ways.
From there, we can assign the 3 topics to the 3 teams in 6 ways, giving us an answer of 540.

However, there's nothing in the original question to suggest that the order of the 3 teams matters. It just says that six students are divided into 3 groups. As such, I have listed all 15 possible ways to do this.

At best this question is ambiguous.

Cheers,
Brent