Error in exercise 1.31 of Casella & Berger?

It seems to me that formula n!/n^{n} for obtaining "the outcome with
average (x1+x2+x3+...+xn)/n" when sampling with replacement from the
set {x1,...,xn} in problem 1.31 of 'Statistical Inference' (2nd ed.)
by Casella and Berger is wrong.

Consider sampling with replacement from {0,1,3,4}. Then,

(x1+...x4)/4=2

but not just the sampling outcome (0,1,3,4), but also the sampling
outcome (0,0,4,4) has the average 2. In this case it is not clear what
"~the~ outcome with average (x1+x2+x3+...+xn)/n" would mean and
interpreting it as "~an~ outcome with average (x1+x2+x3+...+xn)/n"
leads to the number of eligible outcomes being greater than n!.

Appendix I of Hall's 'The Bootstrap and Edgeworth Expansion' which
Casella and Berger cite rules out such situations as being almost
impossible in many settings. However, there is no basis for that
assumption in this particular problem.

[This is a repost of my earlier message on sci.stat.math. My most
humble defence for the sin of multiposting is that of ignorance.]
.

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