【Example 4】Combine $2 n$ new soldiers into $n$ pairs to learn machine gun shooting, (1) one learns to be the main shooter, the other as the assistant; (2) the 2 people are not distinguished as main or assistant, how many ways are there to form the groups?
(1) First, from $2 n$ people, determine $n$ people as the main shooters, there are $C_{2 n}^{n}$ ways to do this. Then consider the pairing of the remaining $n$ people with them, which is equivalent to a full permutation of $n$ people. Therefore, there are
$$
C_{2 n}^{n} \cdot n!=\frac{(2 n)!}{n!}
$$

ways to group them.
(2) This problem is a simple pairing problem, so we know there are
$$
\frac{(2 n)!}{(2!)^{n} \cdot n!}=(2 n-1)(2 n-3) \cdots 3 \cdot 1
$$

different ways to group them (readers can compare this example with Example 8 of Chapter 3).