Hi, I need some help with this perms and combs question,
1) The three judges for Australian Idol have to vote on three singers, listing their order of preference. In how many ways can the judges vote so that any two of them agree in their order of preference, while the third differs?
Thank you!!
Hey! So basically, by forcing two judges to match, that really means that we need
two different arrangements - One held by two judges and something different from the third.
First do the arrangement that is matched:
The second judge can have ANY arrangement
except the one held by the other two judges. So they have 5 choices. Therefore
But, we can also change the judge that doesn't match. There are three judges that could deviate, so we triple our answer.
The final answer is 90 I hope this helps! Hopefully I've interpreted it correctly