20 people came to celebrate their ten-year high school reunion.

Question

20 people came to celebrate their ten-year high school reunion. Each
person shook hands once with all the other persons. How many handshakes were
exchanged at the reunion?

Answer 1

Let's say you had four people at the reunion (ABCD). The handshakes could be represented by:

 

AB, AC, AD, BC, BD, CD.

 

I imagine you are in a course dealing with probability and a lesson dealing with counting (permutations/combinations).

 

This example with four people can be calculated as the "combination" of 4 "things" taken 2 at a time.

 

Depending on your text book this might be represented as ₄C₂ and you likely have a formula for that, something like:

 

_nC_r= n!/(n-r)!r!. 

 

₄C₂= 4(3)/2 = 6

 

Try 5 people (ABCDE)--list the possible handshakes and see if ₅C₂ matches that number.

 

Likely ₂₀C₂ will yield the number of handshakes at a 20 person reunion. Give it a try.