Keywords: combinations and permutations, P-value.
Bundaberg is a coastal town in Queensland. The Bundaberg Cup for greyhounds for 1998 is to be held on 27 June. There are 32 dogs, and there will be four heats of 8 dogs each. Although the dogs are supposed to be randomly assigned to the four heats, it so happens that the leading trainer has four dogs, and exactly one of his dogs is scheduled for each one of the heats. What is the probability of this arrangement, whereby the leadings trainer's dogs do not compete with one another, occuring by chance? Is there any evidence of collusion?
Gordon Smyth, consulting problem.
The total number of ways to assign the dogs to the four heats is
|8! 8! 8! 8!|
and the number of ways with one of the trainer's dogs in each heat
|7! 7! 7! 7!|
so the probability is N.Success/N.Total = 0.114. The probability is small, but not very small, so there is little evidence for collusion.