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Choose a growth rate for the first species: 3 options (fast, medium, slow).
Choose a growth rate for the second species: 2 remaining options.
Choose a growth rate for the third species: 1 remaining option.
The total number of ways to assign the growth rates is calculated by multiplying these choices:
Since all components are distinct, the total number of arrangements is given by:
Arrangements where two specific components (say A and B) are adjacent:
Therefore, the number of arrangements where A and B are adjacent is:
Subtract to find valid arrangements:
Subtract the adjacent cases from the total arrangements:
