A farmer has 12 plots of land, arranged in a row. To ensure viability of the soil, the farmer
never uses two adjacent plots at the same time. This season, the farmer wishes to plant one
plot of each of the following: corn, wheat, soybeans, and rice. Each crop is assigned its own
plot of land. How many ways can the farmer allocate plots of land for these crops?  Choose the correct answer
A) 1680  B) 3024  C) 5040  D) 7920  E) 11880
There is a natural one-to-one correspondence between all choices from a row of 9   plots, and all “legal” choices for the 12 plots in the problem: given a choice of four plots in 9,   insert a fallow plot after each of the first three plots. The number of ways to pick 4 plots of   land from 9 is   􀀀9   4. After the locations of plots have been selected, there are 4! ways to assign   the crops to the plots. The total number of ways is therefore 4!   􀀀9   4   or 3024.   correct answer 3024
<result>B</result>
A farmer has 12 plots of land, arranged in a row. To ensure viability of the soil, the farmer
never uses two adjacent plots at the same time. This season, the farmer wishes to plant one
plot of each of the following: corn, wheat, soybeans, and rice. Each crop is assigned its own
plot of land. How many ways can the farmer allocate plots of land for these crops?