Question-60

counting

There are \(\displaystyle 20\) participants at a chess competition. They each find opponents and start playing. How many possibilities are there for how they matched up, assuming that in each game it does matter who has the white pieces?

\(\frac{20!}{10!}\)

Consider \(\displaystyle 10\) boards that arranged in a straight line, with two places at each board. The total number of ways we can permute the players is \(\displaystyle 20!\). But we can permute the board themselves in \(\displaystyle 10!\) ways. Therefore, we get \(\frac{20!}{10!}\) different match ups.