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counting and probability intermediate

Problem

A farmer's rectangular field is partitioned into by grid of rectangular sections as shown in the figure. In each section the farmer will plant one crop: corn, wheat, soybeans, or potatoes. The farmer does not want to grow corn and wheat in any two sections that share a border, and the farmer does not want to grow soybeans and potatoes in any two sections that share a border. Given these restrictions, in how many ways can the farmer choose crops to plant in each of the four sections of the field?
problem
(A)
(B)
(C)
(D)
Solution
There are possibilities for the top-left section. It follows that the top-right and bottom-left sections each have possibilities, so they have combinations. We have two cases: 1. The top-right and bottom-left sections have the same crop. Note that of the combinations of the top-right and bottom-left sections satisfy this case, from which the bottom-right section has possibilities. Therefore, there are ways in this case. 3. The top-right and bottom-left sections have different crops. Note that of the combinations of the top-right and bottom-left sections satisfy this case, from which the bottom-right section has possibilities. Therefore, there are ways in this case. Together, the answer is
Final answer
C