This question is very similar to one asked on Probability of All Distinct Faces When Six Dice Are Rolled
Now mine has a little spin on it and is: if five fair dice are rolled what is probability that FIVE numbers will appear exactly once?
If anyone is interested, my main goal is making a python script that can calculate the probability, since I'm new to this, this is what I got (though am positive it's wrong):
def numOne(roll): return len([dice1 for dice1 in roll if dice1 == 1]) def numTwo(roll): return len([dice2 for dice2 in roll if dice2 == 2]) def numThree(roll): return len([dice3 for dice3 in roll if dice3 == 3]) def numFour(roll): return len([dice4 for dice4 in roll if dice4 == 4]) def numFive(roll): return len([dice5 for dice5 in roll if dice5 == 5]) def numSix(roll): return len([dice6 for dice6 in roll if dice6 == 6]) r = range(1,7) sample = [(i,j,k,l,m) for i in r for j in r for k in r \ for l in r for m in r] event = [roll for roll in sample if numOne(roll)==1 and numTwo(roll)==1 and numThree(roll)==1 and numFour(roll)==1 and numFive(roll)==1 or numSix(roll)==1] print(len(event) / len(sample))
The output is: 0.417309670781893 or 3245 / 7776