Answer:
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 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.
Answer:
84
Step-by-step explanation:
Quadrants A and C either have the same kind of flower, or they have different flowers.
If quadrants A and C have the same kind of flower, there are 4 ways to choose this flower. There are then 3 ways to choose the flower for quadrant B, and 3 ways to choose the flower for quadrant D, so there are 4 x 3 x 3 = 36 possible ways in this case.
If quadrants A and C have different kinds of flowers, then there are 4 ways to choose the flower for quadrant A, then 3 ways to choose the flower for quadrant C. Then there are 2 ways to choose the flower for quadrant B, and 2 ways to choose the flower for quadrant D, so there are 4 x 3 x 2 x 2 = 48 possible ways in this case.
Therefore, there are a total of 36 + 48 = 84 ways to plant the flowers.
