I am multiplying the probability that the first player doesn't have one of the 24 hands, times the probability that the second player doesn't have it, etc. The denominator in each case is the total number of hands each player can make out of the remaining cards. The numerator is this number minus the 24 hands.


You are correct that depending on which cards each player receives, some of the 24 hands may no longer be possible. I am not taking this into account. That would make the problem even more difficult, and the result would be lower than I have reported.