Posted: Dec 21, 2012 2:08 am
As to coins and dice, coins can be interpreted as d2 dice.
A sequence of all distinct for d(n)? The probability that any one sequence will have all distinct will be 1*(1-1/n)*(1-2/n)*...*(1/n) = n!/(nn) ~ e-n*sqrt(2*pi*n).
Number of faces, probability of an all-faces sequence:
2 0.5
3 0.222222
4 0.09375
5 0.0384
6 0.0154321
7 0.0061199
8 0.00240326
9 0.000936657
10 0.00036288
11 0.000139906
12 0.0000537232
So this method quickly becomes impractical.
A sequence of all distinct for d(n)? The probability that any one sequence will have all distinct will be 1*(1-1/n)*(1-2/n)*...*(1/n) = n!/(nn) ~ e-n*sqrt(2*pi*n).
Number of faces, probability of an all-faces sequence:
2 0.5
3 0.222222
4 0.09375
5 0.0384
6 0.0154321
7 0.0061199
8 0.00240326
9 0.000936657
10 0.00036288
11 0.000139906
12 0.0000537232
So this method quickly becomes impractical.