/** Puzzle from Matthew Roozee:

    Suppose there are exactly 300 m&m’s total in a bag and each one
    is randomly determined to be one of the six colors (all equally
    likely). What is the most likely distribution of m&m’s?

    This is an exact solver for probabilities.
*/
use statistics.frink

bagSize = 300
colors = 6
showApproximations[false]

for [p,n] = partitionsOfSize[bagSize, colors, true]
{
   prob = n
   remain = bagSize      
   for d = colors to 1 step -1
   {
      k = p@(colors-d)
      prob = prob * binomialDensity[k, remain, 1/d]
      remain = remain-k
   }
   println[formatSci[prob,1,15] + "\t$n\t$p"]
}