web2.0calc
 
+0  
 

help

0
286
2
avatar+70 
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?
 Jun 6, 2022

2+0 Answers

 #1
avatar+166 
+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.

 Jun 6, 2022
 #2
avatar+70 
0
Thank you!
Hamburger  Jun 9, 2022

2 Online Users

avatar

Top Users

avatar+129899 CPhill moderator
avatar+37153 ElectricPavlov
avatar+33661 Alan moderator
avatar+15000 asinus moderator
avatar+2511 GingerAle
avatar+2499 Solveit
avatar+1938 NotThatSmart
avatar+1557 parmen
avatar+1521 blackpanther
avatar+1455 kittykat
avatar+1310 learnmgcat

Sticky Topics