'handshake' probability question

[ratindasgupta]

3 groups of 6 individuals meet each other. How many ways can they all shake hands with each other once, provided members of the same group dont shake hands with each other?

Sorry dont have the answer options.

The way i worked it out was let the 3 groups be A, B and C.
So A shakes hands with B in 6! ways
A shakes hands with C in 6! ways
and B shakes hands with C in 6! ways

So i get the answer as (6!)^3

Am i right? i have a sinking feeling i've got the approach completely wrong.

[gabriel]

3 groups of 6 individuals meet each other. How many ways can they all shake hands with each other once, provided members of the same group dont shake hands with each other?

Sorry dont have the answer options.

The way i worked it out was let the 3 groups be A, B and C.
So A shakes hands with B in 6! ways
A shakes hands with C in 6! ways
and B shakes hands with C in 6! ways

So i get the answer as (6!)^3

Am i right? i have a sinking feeling i've got the approach completely wrong.

There are 18 people in all ... among themselves they can shake hand in 18c2 ways ... but in this we also include the shakehands within the group, so you need to subtract that value from 18c2 .. within a group the no. of ways to shake hands is 6c2 .. since there are 3 groups it would be 6c2*3 .... so the final answer should be 18c2-(6c2*3) ..

[ratindasgupta]

Got it.

Thanks gabriel!