Problem 10.1. In an International Peace Congress, presidents of 40 different countries are to meet. The newspaper called “World News” wants to publish, on its cover page, photos of every handshake that will take place between every two presidents at the congress.

Question

Problem 10.1. In an International Peace Congress, presidents of 40 different countries are to meet. The newspaper called “World News” wants to publish, on its cover page, photos of every handshake that will take place between every two presidents at the congress.

10.1.1. How many photos should the newspaper expect to fit on the cover page?
(a) 40 (b) 760 (c) 780 (d) 800 (e) 820 (f) 840

my answer- 40 x 20= 800

Answer 1

you are choosing all possible pairs from 40 to shake hands,

that would be C(40,2) = 780

or

think of it this way:
each of the 40 people can shake hands with 39 other people which is
40x39 = 1560.
BUT, that includes identical pairs,
e.g. A shaking with B is the same as B shaking with A, so we divide 1560 by 2 to get 780