I have 10000 boxes containing 15000 randomly distributed toys, what is the probability that a randomly chosen box has 3 toys in it?
My attempted solution:
I wanted to maximize the entropy given by:
S = -$\Sigma_n$p(n)ln(p(n))
Subject to constraints with Lagrange multipliers. I think there should be two constraint equations, one for the normalization of $p(n)$, although I'm struggling to think of and justify the second constraint equation.