28. (1) How many different ways are there to choose 4 letters from $a, b, b, c, c, c, d, d, d, d$? (2) How many different four-digit numbers can be formed by choosing 4 numbers from $1,2,2,3,3,3,4,4,4,4$?
28. (1) Find the fourth-degree terms of the expansion of $(1+a)\left(1+b+b^{2}\right)\left(1+c+c^{2}+c^{3}\right)\left(1+d+d^{2}+d^{3}+d^{4}\right)$
$$
\begin{array}{l}
a b c d+\left[b^{2}(a c+a d+c d)+c^{2}(a b+a d+b d)+d^{2}(a b+a c+b c)\right] \\
+\left(b^{2} c^{2}+b^{2} d^{2}+c^{2} d^{2}\right)+\left[c^{3}(a+b+d)+d^{3}(a+b+c)\right]+d^{4}
\end{array}
$$

A total of 20 terms, each representing a specific case.
(2) 1234 corresponds to $a b c d$, and from (1) there are 20 terms, but each term in (1) represents one case, while in (2) different numbers can be generated, such as $b^{2} a c$ corresponding to 2213, which corresponds to $\frac{4!}{2!}$ different numbers.
There are a total of $4!+\frac{4!}{2!} \times 9+\frac{4!}{2!2!} \times 3+\frac{4!}{3!} \times 6+1=175$ different numbers.