Question 57
In the mathematical talent show called "The $X^2$-factor", contestants are scored by a panel of 8 judges. Each judge awards a score of 0 ('fail'), $X$ ('pass'), or $X^2$ ('pass with distinction'). Three of the contestants were Ann, Barbara and David. Ann was awarded the same score as Barbara by exactly 4 judges. David declares that he obtained different scores to Ann from at least 4 judges, and also that he obtained different scores to Barbara from at least 4 judges.
In how many ways could scores have been allocated to David, assuming he is telling the truth?
In how many ways could scores have been allocated to David, assuming he is telling the truth?