Example 2 A region is divided into 5 administrative areas. Now we are coloring the map, requiring that two adjacent areas cannot use the same color. There are 4 colors available for selection, then the number of different coloring methods is $\qquad$ (answer with a number).
Solution 1 (Interval Position Classification Discussion Method)
When the 2nd and 4th positions are the same color, there are $4 \times 3 \times 2 \times 2=48$ coloring methods.

When the 2nd and 4th positions are different colors, there are $4 \times 3 \times 2 \times 1 \times 1=24$ coloring methods.

Therefore, there are a total of $48+24=72$ coloring methods that meet the conditions.

Solution 2 (Color Number Classification Discussion Method) Since at least three colors are used for 5 positions.

When 3 colors are used, two colors must be used for two positions each, so the 3rd and 5th positions are the same color, and the 2nd and 4th positions are the same color. This situation has $\mathrm{A}_{4}^{3}=4 \times 3 \times 2=24$ coloring methods;

When 4 colors are used, one color must be used for two positions, so the 2nd and 4th positions or the 3rd and 5th positions are the same color. This situation has $\mathrm{A}_{2}^{1} \mathrm{~A}_{4}^{4}=48$ coloring methods.
Therefore, there are a total of $24+48=72$ coloring methods that meet the conditions.
Solution 3 (Exclusion Method) According to the positions $1,2,3,4,5$, color them sequentially, and assume that the 2nd and 5th positions can be the same color, then there are $4 \times 3 \times 2$ $\times 2 \times 2=96$ coloring methods, but when the 2nd and 5th positions are the same color, the condition is not met. At this time, consider the 2nd and 5th positions as one position, and each position is adjacent to other positions, there are $A_{4}^{4}=24$ coloring methods.
The number of coloring methods that meet the conditions is $96-24=72$.
The above three methods are general methods for solving coloring problems. When using the above three methods to solve problems, choose according to the conditions of the problem, striving to make the problem-solving思路 natural and the calculation simple.

Below are a few more examples to illustrate the application of the above three methods in solving several typical problems.