Solution
= Solution
Moving one ball can destroy at most one empty bin and create at most one empty bin; the net number of empty bins therefore changes by at most one. Thus $f$ has the <bounded differences property> with $c_j=1$ for all $m$ ball coordinates. The upper- and lower-tail forms of the <McDiarmid inequality> give, for $t>0$,
$$
\mathbb P(Z-\mathbb EZ\geq t)
\leq e^{-2t^2/m},
\qquad
\mathbb P(Z-\mathbb EZ\leq-t)
\leq e^{-2t^2/m}.
$$