Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.