=+ This is a special case of the Poisson approximation treated in Example 14.2.2 by the coupling method. In this exercise we attack the birthday problem by the neighborhood method. To get started, let the index set I be the collection of all sets of trials α ⊂ {1,...,n} having |α| = d elements. Let Xα be the indicator of the event that the balls indexed by α all fall into the same box. If S = 

α Xα, then argue that the approximation Pr(S = 0) ≈ e−λ is plausible when

λ =

n d

 1 md−1 .