rianah100 wrote:

Why can't this be-

Select one group out of 6 in 6C1 ways, select one person out of 3 in 3 ways

Then select another group in 5C1 ways, select one person out of 3 in 3 ways

so, combinatons = 6*3*5*3=270

What am I missing?

You double counted the handshakes.

Suppose there are 6 groups - A, B, C, D, E, and F.

There are 3 members in group A, and they are A1, A2, and A3.

There are 3 members in group B, and they are B1, B2, and B3.

First, you pick group A, and pick person A1.

Then you pick group B, and pick person B1.

Again,

first, you pick group B, and pick person B1.

then you pick group A, and pick person A1.

The above two cases have to be counted as one.

Therefore, you have to divide your result by 2.

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