There are three reps from each of the six companies. in how

Question

There are three reps from each of the six companies. in how many ways can they shake hand,without shaking hands with their colleagues from the same company?

Vijo · Answer

The ans is 270.

n people will shake hands with each other in n*(n-1) ways.

3 rep from 6 cos= 18 people in all.

The possible handshakes with each other (all) = 18*17=306

The posible handshakes with own co's rep = 3*2 =6

For all 6 cos total no of handshakes with their own co's rep = 6 *6=36

Thus No of handshakes with each other (excluding own co's rep)= 306-36
 =270

Plz post the answer.(in white)

banerjeea_98 · Answer

Vijo,

I don't understand ur formula of n ppl will shake hand in n(n-1) ways...this way r u saying 2 ppl will shake hands in 2 ways, I wud think it should be one.

I am getting ans to the above ques as 135 ways, exactly half of the OA. Plz explain your eqn...thx

joebaak · Answer

The way I calculated the number of hand shake:

Every person from one company will shake 3 (people) * 5 (companies) = 15 people
And since each company has 3 people
=> 3*15 = 45 hand shake for each company shacking hands with the other people form the 5 other companies
=> and since there are 6 companies
=> 6 * 45 = 270 hand shakes

- Joe

banerjeea_98 · Answer

Your logic is only true if u consider 2 ppl shaking hands as 2 handshakes, in my mind it should be 1 handshake not 2, thus I am getting 135 as ans. I am not sure why we are considering 1 handshake between 2 ppl as 2 handshakes ?? :?

joebaak · Answer

Dear banerjeea_98,

I admire your capabilities of solving problems that I don't even touch, but you are over analsizing the question.
I admit probability, combination and permutation is my weakest point
Just think about the problem in basic mode
1 person hand shakes 15 people
That means 3 people will hand shake 3 * 15 = 45 people
And since there are 6 groups
6 * 45 = 270 people
I hope that will make the solution more clear

Regard - Joe

Vijo · Answer

I think I took a wrong approach.
The no of handshakes between n ppl shud be n(n-1)/2
But then, how is my ans right?
In that way
N ppl will have 18*17/2=153 handshakes in all
n 3 ppl of each co will have 3 handshakesin all which makes 3*6=18 handshakes in all which are to be excluded
thus 153-18=135 which is half of the earlier ans.

Thanks for correcting me.

DLMD plz confirm the ans once again.

vprabhala · Answer

1 person hand shakes 15 people???
i am so lost on thsi one. can you pplease elaborate..

joebaak · Answer

Dear vprabhala,

There is a total of 18 people (in total 3 * 6 = 18) â€“ 3 people from one company = 15 people 
Therefore 1 person will hand shake 15 people hand
In Return 3 people will hand shake 3 * 15 = 45 people
In total there is a total of 6 groups
Therefore 6 * 45 = 270 total hand shake without colleagues from the same company hand shaking
I hope that clear my explanation

There are three reps from each of the six companies. in how

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