Mixing
What is the equation to determine how many combinations can be found when there are two sets with three letters and each can have one of two colors.
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I have two sets (set A, set B) of three letters (X, Y, D). Each letter can have one of two colors (red or blue). How many different combinations are possible. I would like the equation to determine how many.
You could view the problem as follows:
- SET A: [X, Y, D]
- SET B: [X, Y, D]
Each letter can be either red or blue.
One possible combination is
- SET A: [red X, red Y, blue D]
- SET B: [red X, blue Y, red D].
I would like an equation to determine the total of all the different possible combinations.
Just for clarity, another possible combination is:
- SET A: [red X, red Y, red D]
- SET B: [red X, blue Y, blue D].
combinations
asked Jul 30 at 16:44
Daniel Parsons
1
 |Â
show 7 more comments
up vote
0
down vote
favorite
I have two sets (set A, set B) of three letters (X, Y, D). Each letter can have one of two colors (red or blue). How many different combinations are possible. I would like the equation to determine how many.
You could view the problem as follows:
- SET A: [X, Y, D]
- SET B: [X, Y, D]
Each letter can be either red or blue.
One possible combination is
- SET A: [red X, red Y, blue D]
- SET B: [red X, blue Y, red D].
I would like an equation to determine the total of all the different possible combinations.
Just for clarity, another possible combination is:
- SET A: [red X, red Y, red D]
- SET B: [red X, blue Y, blue D].
combinations
asked Jul 30 at 16:44
Daniel Parsons
1
1
Apply multiplication principle to the following set of steps: Choose if setAitemX is red or blue (two options). Choose if setAitemY is red or blue (two options)... ... choose if setBitemD is red or blue (two options). Multiply the number of options available at each step to get the total number of arrangements possible. See rule of product on wikipedia.
– JMoravitz
Jul 30 at 16:50
1
The fact that there are "two sets" and within each set the letters present match is superfluous information. All that matters is the number of items which we are coloring, in this case six items total, and the number of available colors, in this case two colors.
– JMoravitz
Jul 30 at 16:52
1
$2$ options for choosing the color of setAitemX, $2$ options for choosing setAitemY, etc... multiplying the number of choices gives $2times 2times 2timescdots times 2 = 2^6$ is $64$ total possibilities. The whole point of elementary combinatorics is to learn how to count without brute force, never answer questions laboriously by listing out every possible combination if you can help it.
– JMoravitz
Jul 30 at 17:13
Thank you very much for your solution. I believe it is what I am looking for however I still need to list everything out laboriously as I have a sceptical mind by nature. Probably a curse but that is how it is with me. I want to see each of the 64 possibilities listed first before I can trust the mathematical equation. I know I should simply trust the undeniable purity of mathematics but I still feel uncomfortable without having solid evidence that the equation works. Like seeing one orange being added to a basket that already contains an orange, which then gives the result of two oranges.
– Daniel Parsons
Jul 30 at 17:21
Read again the page about the rule of product on wikipedia. Search around this site for more information on it, additional examples, and probably somewhere a proof. A sketch of a proof: consider only two steps at a time, making a table, listing the options for the first step horizontally along the top and the options for the second step vertically along the side. You have then a rectangular grid, showing each possible way the two steps could be completed simultaneously.
– JMoravitz
Jul 30 at 17:26
 |Â
show 7 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have two sets (set A, set B) of three letters (X, Y, D). Each letter can have one of two colors (red or blue). How many different combinations are possible. I would like the equation to determine how many.
You could view the problem as follows:
- SET A: [X, Y, D]
- SET B: [X, Y, D]
Each letter can be either red or blue.
One possible combination is
- SET A: [red X, red Y, blue D]
- SET B: [red X, blue Y, red D].
I would like an equation to determine the total of all the different possible combinations.
Just for clarity, another possible combination is:
- SET A: [red X, red Y, red D]
- SET B: [red X, blue Y, blue D].
combinations
asked Jul 30 at 16:44
Daniel Parsons
1
I have two sets (set A, set B) of three letters (X, Y, D). Each letter can have one of two colors (red or blue). How many different combinations are possible. I would like the equation to determine how many.
You could view the problem as follows:
- SET A: [X, Y, D]
- SET B: [X, Y, D]
Each letter can be either red or blue.
One possible combination is
- SET A: [red X, red Y, blue D]
- SET B: [red X, blue Y, red D].
I would like an equation to determine the total of all the different possible combinations.
Just for clarity, another possible combination is:
- SET A: [red X, red Y, red D]
- SET B: [red X, blue Y, blue D].
combinations
asked Jul 30 at 16:44
Daniel Parsons
1
asked Jul 30 at 16:44
Daniel Parsons
1
asked Jul 30 at 16:44
Daniel Parsons
1
asked Jul 30 at 16:44
Daniel Parsons
1
1
1
Apply multiplication principle to the following set of steps: Choose if setAitemX is red or blue (two options). Choose if setAitemY is red or blue (two options)... ... choose if setBitemD is red or blue (two options). Multiply the number of options available at each step to get the total number of arrangements possible. See rule of product on wikipedia.
– JMoravitz
Jul 30 at 16:50
1
The fact that there are "two sets" and within each set the letters present match is superfluous information. All that matters is the number of items which we are coloring, in this case six items total, and the number of available colors, in this case two colors.
– JMoravitz
Jul 30 at 16:52
1
$2$ options for choosing the color of setAitemX, $2$ options for choosing setAitemY, etc... multiplying the number of choices gives $2times 2times 2timescdots times 2 = 2^6$ is $64$ total possibilities. The whole point of elementary combinatorics is to learn how to count without brute force, never answer questions laboriously by listing out every possible combination if you can help it.
– JMoravitz
Jul 30 at 17:13
Thank you very much for your solution. I believe it is what I am looking for however I still need to list everything out laboriously as I have a sceptical mind by nature. Probably a curse but that is how it is with me. I want to see each of the 64 possibilities listed first before I can trust the mathematical equation. I know I should simply trust the undeniable purity of mathematics but I still feel uncomfortable without having solid evidence that the equation works. Like seeing one orange being added to a basket that already contains an orange, which then gives the result of two oranges.
– Daniel Parsons
Jul 30 at 17:21
Read again the page about the rule of product on wikipedia. Search around this site for more information on it, additional examples, and probably somewhere a proof. A sketch of a proof: consider only two steps at a time, making a table, listing the options for the first step horizontally along the top and the options for the second step vertically along the side. You have then a rectangular grid, showing each possible way the two steps could be completed simultaneously.
– JMoravitz
Jul 30 at 17:26
 |Â
show 7 more comments
1
Apply multiplication principle to the following set of steps: Choose if setAitemX is red or blue (two options). Choose if setAitemY is red or blue (two options)... ... choose if setBitemD is red or blue (two options). Multiply the number of options available at each step to get the total number of arrangements possible. See rule of product on wikipedia.
– JMoravitz
Jul 30 at 16:50
1
The fact that there are "two sets" and within each set the letters present match is superfluous information. All that matters is the number of items which we are coloring, in this case six items total, and the number of available colors, in this case two colors.
– JMoravitz
Jul 30 at 16:52
1
$2$ options for choosing the color of setAitemX, $2$ options for choosing setAitemY, etc... multiplying the number of choices gives $2times 2times 2timescdots times 2 = 2^6$ is $64$ total possibilities. The whole point of elementary combinatorics is to learn how to count without brute force, never answer questions laboriously by listing out every possible combination if you can help it.
– JMoravitz
Jul 30 at 17:13
Thank you very much for your solution. I believe it is what I am looking for however I still need to list everything out laboriously as I have a sceptical mind by nature. Probably a curse but that is how it is with me. I want to see each of the 64 possibilities listed first before I can trust the mathematical equation. I know I should simply trust the undeniable purity of mathematics but I still feel uncomfortable without having solid evidence that the equation works. Like seeing one orange being added to a basket that already contains an orange, which then gives the result of two oranges.
– Daniel Parsons
Jul 30 at 17:21
Read again the page about the rule of product on wikipedia. Search around this site for more information on it, additional examples, and probably somewhere a proof. A sketch of a proof: consider only two steps at a time, making a table, listing the options for the first step horizontally along the top and the options for the second step vertically along the side. You have then a rectangular grid, showing each possible way the two steps could be completed simultaneously.
– JMoravitz
Jul 30 at 17:26
1
1
Apply multiplication principle to the following set of steps: Choose if setAitemX is red or blue (two options). Choose if setAitemY is red or blue (two options)... ... choose if setBitemD is red or blue (two options). Multiply the number of options available at each step to get the total number of arrangements possible. See rule of product on wikipedia.
– JMoravitz
Jul 30 at 16:50
Apply multiplication principle to the following set of steps: Choose if setAitemX is red or blue (two options). Choose if setAitemY is red or blue (two options)... ... choose if setBitemD is red or blue (two options). Multiply the number of options available at each step to get the total number of arrangements possible. See rule of product on wikipedia.
– JMoravitz
Jul 30 at 16:50
1
1
The fact that there are "two sets" and within each set the letters present match is superfluous information. All that matters is the number of items which we are coloring, in this case six items total, and the number of available colors, in this case two colors.
– JMoravitz
Jul 30 at 16:52
The fact that there are "two sets" and within each set the letters present match is superfluous information. All that matters is the number of items which we are coloring, in this case six items total, and the number of available colors, in this case two colors.
– JMoravitz
Jul 30 at 16:52
1
1
$2$ options for choosing the color of setAitemX, $2$ options for choosing setAitemY, etc... multiplying the number of choices gives $2times 2times 2timescdots times 2 = 2^6$ is $64$ total possibilities. The whole point of elementary combinatorics is to learn how to count without brute force, never answer questions laboriously by listing out every possible combination if you can help it.
– JMoravitz
Jul 30 at 17:13
$2$ options for choosing the color of setAitemX, $2$ options for choosing setAitemY, etc... multiplying the number of choices gives $2times 2times 2timescdots times 2 = 2^6$ is $64$ total possibilities. The whole point of elementary combinatorics is to learn how to count without brute force, never answer questions laboriously by listing out every possible combination if you can help it.
– JMoravitz
Jul 30 at 17:13
Thank you very much for your solution. I believe it is what I am looking for however I still need to list everything out laboriously as I have a sceptical mind by nature. Probably a curse but that is how it is with me. I want to see each of the 64 possibilities listed first before I can trust the mathematical equation. I know I should simply trust the undeniable purity of mathematics but I still feel uncomfortable without having solid evidence that the equation works. Like seeing one orange being added to a basket that already contains an orange, which then gives the result of two oranges.
– Daniel Parsons
Jul 30 at 17:21
Thank you very much for your solution. I believe it is what I am looking for however I still need to list everything out laboriously as I have a sceptical mind by nature. Probably a curse but that is how it is with me. I want to see each of the 64 possibilities listed first before I can trust the mathematical equation. I know I should simply trust the undeniable purity of mathematics but I still feel uncomfortable without having solid evidence that the equation works. Like seeing one orange being added to a basket that already contains an orange, which then gives the result of two oranges.
– Daniel Parsons
Jul 30 at 17:21
Read again the page about the rule of product on wikipedia. Search around this site for more information on it, additional examples, and probably somewhere a proof. A sketch of a proof: consider only two steps at a time, making a table, listing the options for the first step horizontally along the top and the options for the second step vertically along the side. You have then a rectangular grid, showing each possible way the two steps could be completed simultaneously.
– JMoravitz
Jul 30 at 17:26
Read again the page about the rule of product on wikipedia. Search around this site for more information on it, additional examples, and probably somewhere a proof. A sketch of a proof: consider only two steps at a time, making a table, listing the options for the first step horizontally along the top and the options for the second step vertically along the side. You have then a rectangular grid, showing each possible way the two steps could be completed simultaneously.
– JMoravitz
Jul 30 at 17:26
 |Â
show 7 more comments
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1
Apply multiplication principle to the following set of steps: Choose if setAitemX is red or blue (two options). Choose if setAitemY is red or blue (two options)... ... choose if setBitemD is red or blue (two options). Multiply the number of options available at each step to get the total number of arrangements possible. See rule of product on wikipedia.
– JMoravitz
Jul 30 at 16:50
1
The fact that there are "two sets" and within each set the letters present match is superfluous information. All that matters is the number of items which we are coloring, in this case six items total, and the number of available colors, in this case two colors.
– JMoravitz
Jul 30 at 16:52
1
$2$ options for choosing the color of setAitemX, $2$ options for choosing setAitemY, etc... multiplying the number of choices gives $2times 2times 2timescdots times 2 = 2^6$ is $64$ total possibilities. The whole point of elementary combinatorics is to learn how to count without brute force, never answer questions laboriously by listing out every possible combination if you can help it.
– JMoravitz
Jul 30 at 17:13
Thank you very much for your solution. I believe it is what I am looking for however I still need to list everything out laboriously as I have a sceptical mind by nature. Probably a curse but that is how it is with me. I want to see each of the 64 possibilities listed first before I can trust the mathematical equation. I know I should simply trust the undeniable purity of mathematics but I still feel uncomfortable without having solid evidence that the equation works. Like seeing one orange being added to a basket that already contains an orange, which then gives the result of two oranges.
– Daniel Parsons
Jul 30 at 17:21
Read again the page about the rule of product on wikipedia. Search around this site for more information on it, additional examples, and probably somewhere a proof. A sketch of a proof: consider only two steps at a time, making a table, listing the options for the first step horizontally along the top and the options for the second step vertically along the side. You have then a rectangular grid, showing each possible way the two steps could be completed simultaneously.
– JMoravitz
Jul 30 at 17:26