Example 4 Plant all 3 types of crops in the 5 plots of experimental fields as shown in Figure 4, with each plot planting one type of crop and no two adjacent plots can plant the same type of crop. How many different planting methods are there?
Solution (Permutation Method): Planting in the order of $1,2,3,4,5$, there are $3 \times 2 \times 2 \times 2 \times 2=48$ ways to plant. However, among these methods, there are cases where only 2 types of crops are planted. When planting two types of crops, there are $A_{3}^{2}=6$ ways, which does not meet the conditions. The number of ways that meet the conditions is $48-6=42$.

Comment: This problem can also be solved using the method of classifying by interval positions.

