Example 2.1.2 Unit $A$ has 7 representatives, and Unit $B$ has 3 representatives. They are to be arranged in a row for a group photo, with the requirement that the 3 representatives from Unit $B$ must stand together. How many different arrangements are possible?
Solution: First, consider the 3 people from unit $B$ as one element and arrange them with the 7 people from unit $A$, which gives a total of $(7+1)!=8!$ arrangements. Then, the 3 people from unit $B$ can still be arranged among themselves in $3!$ ways. According to the multiplication principle, the total number of arrangement schemes is $8! \times 3!$.