Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Over the summer a bunch of math teachers from different schools got together for a BBQ. Not one of the teachers knew each other and greets each other with a hearty handshake. How many handshakes will occur at the party if every one of the 15 math teachers shakes hands with each of the others?

show work

Sagot :

AL2006
The first partner in the handshake can be any one of 15 people. 
The second partner can be any one of 14 people. 
So the total number of possible arrangements is (15 x 14) = 210 .

BUT . . . .

If Mr. Smith and Mr. Jones are shaking hands, it doesn't matter which one is the first partner and which one is the second partner ...  It's the same handshake either way.

That number of ' 210 ' up above counted both ways separately.  The real number of handshakes between different people is half of that   210/2 = 105 handshakes.
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.