Example 1-20 Red, yellow, blue, and green flags, four of each color, totaling 16 flags, are to be arranged in a row. How many different arrangements are possible?
Considering the four flags of each color (red, yellow, blue, green) are indistinguishable, we have
$$
\frac{16!}{(4!)^{4}}=63063000
$$
$(4!)^{4}$ is due to the repetition caused by the four indistinguishable flags of each color.