【Example 1】In a class, there are 28 boys and 22 girls. To elect 5 people to take on different class committee roles, it is hoped that the 5 people will include both boys and girls. How many different election outcomes are possible?
Solution: Since the number of ways to "select any five people" is $A_{50}^{5}$, and the number of ways to select all boys or all girls are $A_{28}^{5}$ and $A_{22}^{5}$ respectively, the number of possible election outcomes under the desired election method is
$$
A_{50}^{5}-A_{28}^{5}-A_{22}^{5}=239297520
$$

possible election results.