During football season, 25 teams are ranked by three reporters (Alice, Bob and Cecil). Each reporter assigned all 25 integers (1 through 25) when ranking the twenty-five teams. A team earns 25 points for each first-place ranking, 24 points for each second-place ranking, and so on, getting one point for a 25th place ranking. The Hedgehogs earned 27 total points from the three reporters. How many different ways could the three reporters have assigned their rankings for the Hedgehogs?

Hamburger Jun 6, 2022

#1**+1 **

We can view the problem as if there are 27 dots in a row split into three sections by two dividers. There would be C(26, 2) to choose where to place the dividers. That is equivilant to \(\frac{26!}{2!24!}=\frac{25\cdot26}{2}=325\), so that is our answer.

RainbowSquirrel53 Jun 6, 2022