Answer:
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Explanation:
Call the quadrants I, II, III, and IV, counterclockwise, and the kinds of flowers A, B, C, and D.
Start by assigning a flower of kind A to quadrant I.
Then, quadrant II can have flower B, C, or D.
- If it is B, then quadrant III can have either A, C, or D. If it is
If quadrant III has A, then quadrant IV can have either B, C, or D. That is 3 different gardens.
If quadrant III has C, then quadrant IV can have either B or D. That is 2 different gardens.
If quadrant III has D, then quadrant IV can either either B or C. That is 2 different gardens.
Those are all the possible different gardens if A is assigned to quadrant I and B is assigned to quadrant II: 3 + 2 + 2 = 7.
Working yet with A in quadrant I but assigning C to quadrant II, you can make the same reasoning as above to get other 7 gardens.
The same with A in quadrant I but D in quadrant II, other 7 different gardents.
In total, you find 7 × 3 = 21 different gardens when flowers of kind A are assingned to quadrant I.
Starting with a flower of kind B in quadrant I, there will be other 21 different gardens. The same for C and D. Then, in total, there are 4 × 21 = 84 different possible gardens.
