Maths Coursework
Emma's Dilemma
Emma's Dilemma
The name Lucy has got four letters with none of the letters repeated. This means that when I come to choosing a letter I have a choice of four then 3 then 2 then 1 if I write those out and multiply them together I will get the number of arrangements. Which is 4 x 3 x 2 x 1, which also can also be written as 4!
In my coursework I am going to show the different arrangements of Lucy's name and I am going to find out how many how many arrangements there can be for any name even if the name has more than one letter that is repeated. I will do this by using a formula that I am going to find. Here is a list of all of the arrangements of Lucy's name:
. LUCY
2. LUYC
3. LCUY
4. LCYU
5. LYUC
6. LYCU
7. ULYC
8. UCLY
9. ULCY
0. UCYL
1. UYCL
2. UYLC
3. CYLU
4. CYUL
5. CULY
6. CUYL
7. CLUY
8. CLYU
9. YLUC
20. YLCU
21. YCUL
22. YCLU
23. YULC
24. YUCL
There are 24 different arrangements of Lucy because first I had 4 to choose form then I had 3 to choose from then I had 2 to choose from then I had 1 to choose from. So if I times 4 x 3 x 2 x 1 I will get 24. This is the same as 4! This sign is called factorial. And this is another way to find out how many arrangements there are in Lucy's name, this method is called factorial. With this method I do not have to list all of the different ways of Lucy's name. I will just have to find out how many different arrangements there are. The problem with this method is that if I had 1 letter or more repeated then this method would not work. To find out how many combinations there are in a persons name with no letters repeated is n! So if I had a 3-letter word with none repeated then I would do 3! Which is the same as 3 x 2 x 1, which are 6.
Emma's Dilemma
Emma's Dilemma
The name Lucy has got four letters with none of the letters repeated. This means that when I come to choosing a letter I have a choice of four then 3 then 2 then 1 if I write those out and multiply them together I will get the number of arrangements. Which is 4 x 3 x 2 x 1, which also can also be written as 4!
In my coursework I am going to show the different arrangements of Lucy's name and I am going to find out how many how many arrangements there can be for any name even if the name has more than one letter that is repeated. I will do this by using a formula that I am going to find. Here is a list of all of the arrangements of Lucy's name:
. LUCY
2. LUYC
3. LCUY
4. LCYU
5. LYUC
6. LYCU
7. ULYC
8. UCLY
9. ULCY
0. UCYL
1. UYCL
2. UYLC
3. CYLU
4. CYUL
5. CULY
6. CUYL
7. CLUY
8. CLYU
9. YLUC
20. YLCU
21. YCUL
22. YCLU
23. YULC
24. YUCL
There are 24 different arrangements of Lucy because first I had 4 to choose form then I had 3 to choose from then I had 2 to choose from then I had 1 to choose from. So if I times 4 x 3 x 2 x 1 I will get 24. This is the same as 4! This sign is called factorial. And this is another way to find out how many arrangements there are in Lucy's name, this method is called factorial. With this method I do not have to list all of the different ways of Lucy's name. I will just have to find out how many different arrangements there are. The problem with this method is that if I had 1 letter or more repeated then this method would not work. To find out how many combinations there are in a persons name with no letters repeated is n! So if I had a 3-letter word with none repeated then I would do 3! Which is the same as 3 x 2 x 1, which are 6.
