Don's pot plants: A combinatorics problem
Don's pot plants: A combinatorics problem
Method 2
Method 1
Click start to begin
Click start to begin
Start
Start
Start
Method 1
Don has four pot plants which he arranges in a straight line. There is one pot each of herbs, tomatoes, bamboo and diasies. Let's begin by listing them alphabetically. We'll also colour the pots to make distinguishing between them easier.
Next
Method 1
We'll start with all of the options where the left-most pot is bamboo.
Consider:
- How many possibilities would there be if the herbs came next?
- How many possibilities would there be if the tomatoes came next?
- How many possibilities would there be if the daisies came next?
PREVIOUS
Next
Method 1
Every time we change the first pot plant, we'll get the same number of different possibilities.
PREVIOUS
Next
Method 1
There are 4 different ways to select the plant for the first (left-most) position. For each possible plant in the first position there are 3 possible plants that can be placed in the second position, followed by 2 possible plants for the 3rd position, and 1 remaining plant for the fourth position. All together, there are 4 x 3 x 2 x 1 = 24 ways to arrange Don's pot plants.
PREVIOUS
Method 2
Don has four pot plants which he arranges in a straight line. There is one pot each of herbs, tomatoes, bamboo and diasies. Let's begin by colouring the pots to make distinguishing between them easier.
Next
Method 2
Put the bamboo down. Put the daisies either to the left or to the right of the bamboo. At this stage we know there are 2 possible positions for the daisies, relative to the bamboo.
Step 1.
1.
Step 2.
2.
PREVIOUS
Next
Method 2
So far, we have placed placed bamboo and daisies in some order. We can now put the tomatoes in one of 3 different positions relative to the plants already there.
Step 3.
3.
PREVIOUS
Next
Method 2
With 2 ways to arrange the bamboo and daisies, and 3 ways to arrange the tomatoes around them. This means there are 2 x 3 = 6 different arrangements for these three plants. The herbs can now be placed in one of 4 different positions relative to the other plants.
Step 4.
4.
PREVIOUS
Next
Method 2
Therefore there are 2 x 3 x 4 = 24 ways to arrange Don's pot plants.
PREVIOUS
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Transcript
Don's pot plants: A combinatorics problem
Don's pot plants: A combinatorics problem
Method 2
Method 1
Click start to begin
Click start to begin
Start
Start
Start
Method 1
Don has four pot plants which he arranges in a straight line. There is one pot each of herbs, tomatoes, bamboo and diasies. Let's begin by listing them alphabetically. We'll also colour the pots to make distinguishing between them easier.
Next
Method 1
We'll start with all of the options where the left-most pot is bamboo.
Consider:
PREVIOUS
Next
Method 1
Every time we change the first pot plant, we'll get the same number of different possibilities.
PREVIOUS
Next
Method 1
There are 4 different ways to select the plant for the first (left-most) position. For each possible plant in the first position there are 3 possible plants that can be placed in the second position, followed by 2 possible plants for the 3rd position, and 1 remaining plant for the fourth position. All together, there are 4 x 3 x 2 x 1 = 24 ways to arrange Don's pot plants.
PREVIOUS
Method 2
Don has four pot plants which he arranges in a straight line. There is one pot each of herbs, tomatoes, bamboo and diasies. Let's begin by colouring the pots to make distinguishing between them easier.
Next
Method 2
Put the bamboo down. Put the daisies either to the left or to the right of the bamboo. At this stage we know there are 2 possible positions for the daisies, relative to the bamboo.
Step 1.
1.
Step 2.
2.
PREVIOUS
Next
Method 2
So far, we have placed placed bamboo and daisies in some order. We can now put the tomatoes in one of 3 different positions relative to the plants already there.
Step 3.
3.
PREVIOUS
Next
Method 2
With 2 ways to arrange the bamboo and daisies, and 3 ways to arrange the tomatoes around them. This means there are 2 x 3 = 6 different arrangements for these three plants. The herbs can now be placed in one of 4 different positions relative to the other plants.
Step 4.
4.
PREVIOUS
Next
Method 2
Therefore there are 2 x 3 x 4 = 24 ways to arrange Don's pot plants.
PREVIOUS