Example 1-13 5 flags of different colors, 20 different kinds of potted flowers, arranged in a form with two flags at the ends and 3 potted flowers in the middle. How many different arrangements are there?
The number of permutations of taking 2 flags out of 5 is
$$
P(5,2)=5 \times 4=20
$$
The number of permutations of taking 3 flowers out of 20 is
$$
P(20,3)=20 \times 19 \times 18=6840
$$

According to the multiplication rule, the total number of schemes is
$$
N=20 \times 6840=136800
$$