At a party with 16 guests, every person shakes hands with 3 other guests. How many handshakes take place?

Question

 The answer is not 6 choose 3.

I need the answer by tomorrow.

Answer 1

Hi Martina--

 

I get 24. If you divide the guests into groups of 4, and have everyone in the group shake with everyone else in that group, you get 6:

 

A shakes with B,C, and D

B shakes with C and D

C shakes with D

 

Everyone has shaken with everyone in their group one time. Do the same thing in each of the 4 groups and you get 24.

 

There are other ways to set it up, but the answer SHOULD always be 24.

 

Hope this helps!

 

Matt in New York