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To find out all the different combinations of hats that each elf can wear, we can use factorials to answer this question. There are 5 hats, and 3 of them are red and 2 of them are green. So we would take the number of hats, which is 5 and divide it by the number of red hats (3) and then the number of green hats (2). This gave me an expression of 5!÷3!÷2!. This gave me an answer of 10. Therefore, the amount of photos that can be taken would be 10. I am not sure if this is correct.
Here's how I solved the question: So first I found the amount of way you could distribute the coal if you gave Zeta one: To find the different ways I wrote Z ( Zeta) E ( Eta) T ( Theta) and wrote down the numbers that work which was a total of 8 different numbers. I soon found that everytime I gave Zeta one more piece of coal the amount of ways you could distribute the coalwent down by one, so in the end I came up with: 1 (8) 2 (7) 3 (6) 4 (5) 5 (4) 6 (3) 7 (2)
Then I added the numbers in the brackets together to get 35 There are 35 different ways to distribute the coal.
Grade 8 POTW: How I did it was to first figure out if the question was stating permutation(Order matters) or Combination(Order does not matter). I found it to be permutation, meaning that 1,8,1 and 1,1,8 are different choices. When I look at it, the first person can only get from 1 coal to 8 coal. When I ordered it, I found that it was like this: 1(8) 2(7) 3(6) 4(5) 5(4) 6(3) 7(2) 8(1) Then, I would be able to add it to figure out all of the choices. 1+2+3+4+5+6+7+8=36.
Therefore, I got a total of 36 different ways to give coal to the NAUGHTY elves.
P.S. to the elves: Have a nice christmas present! XD
Grade 7 POTW: HOW DID I FIGURE OUT GRADE 8 BEFORE THIS?! Anyways, I have a special formula to figure this question out. Because there are 5 different hats, to figure out how many pictures can be taken I would use 5!(5*4*3*2*1). This would give me 120, but of course that is not possible, since there are duplicates. Now, I have to use another formula to try to figure the real answer out. Since there are 3 red hats, I have to use 3!, and since there are 2 green hats, I have to have 2!. So now I use 120 to divide by 3!, and then 2!.
My equation would 120/6/2. This equals to 10.
Therefore, 10 different photos could be taken. -Alan
Using Alan's help I know the formula to figuring out the answer. I first need to figure out what 5! is. Then I need to divide that by 3! and 2!. So, first of all, 5!. 5 x 4 x 3 x 2 x 1 = 120 which is what 5! is. 3! is 6 as 3 x 2 x 1 is 6 and 2! is 2. So now i need to divide 120 by 6 then 2. 120 / 6 = 20 and 20 / 2 is 10. This means that there are 10 combinations of hats that the elfs can wear.
Grade 7 POTW: I solved this in a slightly different method. Immediately we can notice that the words identical except color. There are only 2 colors possible, red and green. This gives us 2 different types of hats and 5 elves. Therefore now we can simply have each elf taking a photo with each type of hat. So 2x5=10. Therefore 10 photos can be took. I'm not sure if this is a correct way to solve this, nor if it makes any sense.
Grade 7 POTW~ I think that 10 different photos can be taken. I made a tree chart which shows that an elf can wear either a red hat, of a green hat. This gave me 10 different outcomes for the photos that can be taken.
Here is how I went about solving the Grade 7 POTW: I started off by seeing that there were five hats. And after reading the question, I understood that it was asking for how many possible combinations the hats could be placed in. So I immediately went to the expression 5!. This essentially means (5*4*3*2*1) which equals 120. This was the total but now I have to focus on each type of hat. Since there are three red hats, I did 3! (equal to 6) and the two green hats resulted in me calculating 2! (equal to 2). So the final expression would be (120/6/2). 120 divided by 6 equals 20, and 20 divided by 2 gives us a final quotient of 10. Therefore, 10 different photos could be taken.
I used a tree chart staring off the first row with the names of the elves. I then branched out into red and green hats. This means since 5*2=10, there are 10 ways to set up the photo. However, I originally thought that the answer was 6 as 3*2=6 but I then realized my flaws.
To solve this problem I first found the pattern between the numbers, To do this I wrote all the numbers out in a pattern, if one was the starting number for Zeta, and Eta and Theta got other numbers which would add up to 10, there would be 8 ways, 118, 127, 136, 145, 154, 163, 172, 181. I then did this with 2 and got 7 ways 217, 226, 235, 244, 253, 262, 271. Then with 3 and got 6 ways, as I continued I saw a pattern and was able to get the answer. 1:8 2:7 3:6 4:5 5:4 6:3 7:2 8:1 After adding these all up, I got the answer of 36, so there are 36 ways he can give them coal.
POTW #14 for Grade 8 At first I started listing out all of the different ways Santa could give the triplets gold, but after listing about 25 or more ways, I realized that the list could go on forever. It was then that Vivian showed me a faster more effective way to get the answer, so thank you Vivian. Ultimately, I got the answer of 36 different ways. I completed this question i my Math Notebook.
I had an awkwardly hard time trying t solve this question. First what I checked if the order of the numbers matters, and I found out that yes, it does matter that 1,8,1 and 1,1,8 are different choices. So after calculating, the first elf can only get from 1 coal to 8 coal. When I ordered it, the following were the results: 1 (8), 2 (7), 3 (6), 4 (5), 5 (4), 6 (3), 7 (2) and 8 (1) Therefore, I added it to figure out all of the choices. 1+2+3+4+5+6+7+8=36.
Hence I got a total of 36 different ways to give coal to the three cheeky elves.
I got the answer of 10 for the POTW. I made a tree diagram that practically summed up: Each elf wore both coloured hats once, which is 5*2=10. Therefore my answer is 10.
Example Elf 1 Elf 2 Green Elf 3 Elf 4 Elf 5
Just imagine that with the each of the "Elf" labels connecting to green. And thus, I got the answer of 10.
Just a little something: I'm actually not sure but... if you read the question carefully, it says: How many different photos can be taken? We can simply say how many photos you take is how many different photos that are taken because someone will move in each photo (or something), thus making it different from the other photos. (I say a smile faltering is also a difference!)
Well the way i did this was pretty simple. Since there are 2 different colours and 5 different elf, each elf can wear either red or green. So this is actually the same just the simple equation 5 * 2, in which case we'd get 10. This means that there are a total of 10 different combinations.
Grade 8 POTW. There are 36 different ways. This is because while creating a tree diagram I noticed that for the first elf there are 8 different ways to arrange it. Then while doing that I noticed that after every "time" the amount of options would decrease by 1. (eg. if the first elf gets 8 pieces of coal, there are 8 different ways to arrange it. If he gets 2 pieces of coal there are 7 different ways etc.). This becomes 8+7+6+5+4+3+2+1=36 so there are 36 different combinations.
I originally thought that the formula for this question would be 5! but I realized that this was wrong as there are duplicate hats. Since there are 2 green hats and 3 reds hats, I have to use 2! and 3!.
The real formula is 5! / 3! / 2!. 5! = 5 * 4 * 3 * 2 * 1 = 120 3! = 3 * 2 * 1 = 6 2! = 2 * 1 = 2
120 / 6 / 2 = 10
There are 10 possible ways the photos can be taken.
Sorry I was late to write this, oops... I got the answer of 10. This was quite simple, for I just had to multiply the amount of people by the number of different colour of hats. 5 * 2 = 10. Therefore, there are 10 ways.
Because there are 5 elves and 2 different types of hats that could be worn, the formula is 5*2, which equals 10. This means that 10 different photos can be taken
To find out all the different combinations of hats that each elf can wear, we can use factorials to answer this question. There are 5 hats, and 3 of them are red and 2 of them are green. So we would take the number of hats, which is 5 and divide it by the number of red hats (3) and then the number of green hats (2). This gave me an expression of 5!÷3!÷2!. This gave me an answer of 10.
ReplyDeleteTherefore, the amount of photos that can be taken would be 10.
I am not sure if this is correct.
Here's how I solved the question:
ReplyDeleteSo first I found the amount of way you could distribute the coal if you gave Zeta one:
To find the different ways I wrote Z ( Zeta) E ( Eta) T ( Theta) and wrote down the numbers that work which was a total of 8 different numbers.
I soon found that everytime I gave Zeta one more piece of coal the amount of ways you could distribute the coalwent down by one, so in the end I came up with:
1 (8)
2 (7)
3 (6)
4 (5)
5 (4)
6 (3)
7 (2)
Then I added the numbers in the brackets together to get 35
There are 35 different ways to distribute the coal.
I missed 8 (1)
DeleteSo there are actually 36 different ways
I got a total of 35 different ways to "spread the love" with coal to the three elves. XD.
ReplyDeleteGrade 8 POTW:
ReplyDeleteHow I did it was to first figure out if the question was stating permutation(Order matters) or Combination(Order does not matter). I found it to be permutation, meaning that 1,8,1 and 1,1,8 are different choices. When I look at it, the first person can only get from 1 coal to 8 coal. When I ordered it, I found that it was like this:
1(8)
2(7)
3(6)
4(5)
5(4)
6(3)
7(2)
8(1)
Then, I would be able to add it to figure out all of the choices. 1+2+3+4+5+6+7+8=36.
Therefore, I got a total of 36 different ways to give coal to the NAUGHTY elves.
P.S. to the elves: Have a nice christmas present! XD
Grade 7 POTW:
ReplyDeleteHOW DID I FIGURE OUT GRADE 8 BEFORE THIS?! Anyways, I have a special formula to figure this question out. Because there are 5 different hats, to figure out how many pictures can be taken I would use 5!(5*4*3*2*1). This would give me 120, but of course that is not possible, since there are duplicates.
Now, I have to use another formula to try to figure the real answer out. Since there are 3 red hats, I have to use 3!, and since there are 2 green hats, I have to have 2!. So now I use 120 to divide by 3!, and then 2!.
My equation would 120/6/2. This equals to 10.
Therefore, 10 different photos could be taken.
-Alan
Using Alan's help I know the formula to figuring out the answer. I first need to figure out what 5! is. Then I need to divide that by 3! and 2!. So, first of all, 5!. 5 x 4 x 3 x 2 x 1 = 120 which is what 5! is. 3! is 6 as 3 x 2 x 1 is 6 and 2! is 2. So now i need to divide 120 by 6 then 2. 120 / 6 = 20 and 20 / 2 is 10. This means that there are 10 combinations of hats that the elfs can wear.
ReplyDeleteGrade 7 POTW:
ReplyDeleteI solved this in a slightly different method. Immediately we can notice that the words identical except color. There are only 2 colors possible, red and green. This gives us 2 different types of hats and 5 elves. Therefore now we can simply have each elf taking a photo with each type of hat. So 2x5=10. Therefore 10 photos can be took. I'm not sure if this is a correct way to solve this, nor if it makes any sense.
Grade 7 POTW~ I think that 10 different photos can be taken. I made a tree chart which shows that an elf can wear either a red hat, of a green hat. This gave me 10 different outcomes for the photos that can be taken.
ReplyDeleteHere is how I went about solving the Grade 7 POTW:
ReplyDeleteI started off by seeing that there were five hats. And after reading the question, I understood that it was asking for how many possible combinations the hats could be placed in. So I immediately went to the expression 5!. This essentially means (5*4*3*2*1) which equals 120. This was the total but now I have to focus on each type of hat. Since there are three red hats, I did 3! (equal to 6) and the two green hats resulted in me calculating 2! (equal to 2). So the final expression would be (120/6/2). 120 divided by 6 equals 20, and 20 divided by 2 gives us a final quotient of 10. Therefore, 10 different photos could be taken.
I used a tree chart staring off the first row with the names of the elves. I then branched out into red and green hats. This means since 5*2=10, there are 10 ways to set up the photo. However, I originally thought that the answer was 6 as 3*2=6 but I then realized my flaws.
ReplyDeleteTo solve this problem I first found the pattern between the numbers, To do this I wrote all the numbers out in a pattern, if one was the starting number for Zeta, and Eta and Theta got other numbers which would add up to 10, there would be 8 ways, 118, 127, 136, 145, 154, 163, 172, 181. I then did this with 2 and got 7 ways 217, 226, 235, 244, 253, 262, 271. Then with 3 and got 6 ways, as I continued I saw a pattern and was able to get the answer.
ReplyDelete1:8
2:7
3:6
4:5
5:4
6:3
7:2
8:1
After adding these all up, I got the answer of 36, so there are 36 ways he can give them coal.
There are 10 different ways to do it because I made a Tree chart and I got 10 different ways.
ReplyDeletePOTW #14 for Grade 8
ReplyDeleteAt first I started listing out all of the different ways Santa could give the triplets gold, but after listing about 25 or more ways, I realized that the list could go on forever. It was then that Vivian showed me a faster more effective way to get the answer, so thank you Vivian. Ultimately, I got the answer of 36 different ways. I completed this question i my Math Notebook.
I did not really understand how to solve the POTW.
ReplyDeleteYou could try to use a tree chart
DeleteI had an awkwardly hard time trying t solve this question. First what I checked if the order of the numbers matters, and I found out that yes, it does matter that 1,8,1 and 1,1,8 are different choices. So after calculating, the first elf can only get from 1 coal to 8 coal. When I ordered it, the following were the results:
ReplyDelete1 (8), 2 (7), 3 (6), 4 (5), 5 (4), 6 (3), 7 (2) and 8 (1)
Therefore, I added it to figure out all of the choices. 1+2+3+4+5+6+7+8=36.
Hence I got a total of 36 different ways to give coal to the three cheeky elves.
I got the answer of 10 for the POTW. I made a tree diagram that practically summed up: Each elf wore both coloured hats once, which is 5*2=10. Therefore my answer is 10.
ReplyDeleteExample
Elf 1
Elf 2
Green Elf 3
Elf 4
Elf 5
Just imagine that with the each of the "Elf" labels connecting to green. And thus, I got the answer of 10.
Just a little something: I'm actually not sure but... if you read the question carefully, it says:
How many different photos can be taken?
We can simply say how many photos you take is how many different photos that are taken because someone will move in each photo (or something), thus making it different from the other photos. (I say a smile faltering is also a difference!)
Interesting interpretation of the wording Cindy.
DeleteWell the way i did this was pretty simple. Since there are 2 different colours and 5 different elf, each elf can wear either red or green. So this is actually the same just the simple equation 5 * 2, in which case we'd get 10. This means that there are a total of 10 different combinations.
ReplyDeleteI got the answer 10 for the Grade 7 POTW. I finished it on paper.
ReplyDeleteThere are 10 different possibilities because each elf would wear each colour of festive hat, so 5 elves x 2 hat colours= 10 possibilities
ReplyDeleteFor the POTW, I got 10, all I really did was 2*5 in order to get 10. This is because there are 2 types of colors and 5 people,so 2*5 is 10.
ReplyDeleteGrade 8 POTW. There are 36 different ways. This is because while creating a tree diagram I noticed that for the first elf there are 8 different ways to arrange it. Then while doing that I noticed that after every "time" the amount of options would decrease by 1. (eg. if the first elf gets 8 pieces of coal, there are 8 different ways to arrange it. If he gets 2 pieces of coal there are 7 different ways etc.). This becomes 8+7+6+5+4+3+2+1=36 so there are 36 different combinations.
ReplyDeleteI originally thought that the formula for this question would be 5! but I realized that this was wrong as there are duplicate hats. Since there are 2 green hats and 3 reds hats, I have to use 2! and 3!.
ReplyDeleteThe real formula is 5! / 3! / 2!.
5! = 5 * 4 * 3 * 2 * 1 = 120
3! = 3 * 2 * 1 = 6
2! = 2 * 1 = 2
120 / 6 / 2 = 10
There are 10 possible ways the photos can be taken.
My answer was 10. Since there are 5 elves and 2 different colour hats, you do 5*2 which gets you 10.
ReplyDeleteMy answer is 36 ways. This is because I listed how many times I can get 10 with 3 numbers added together. The list is on a scrap piece of paper.
ReplyDeleteSorry I was late to write this, oops...
ReplyDeleteI got the answer of 10. This was quite simple, for I just had to multiply the amount of people by the number of different colour of hats. 5 * 2 = 10.
Therefore, there are 10 ways.
Because there are 5 elves and 2 different types of hats that could be worn, the formula is 5*2, which equals 10. This means that 10 different photos can be taken
ReplyDelete