• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
• Level: GCSE
• Subject: Maths
• Word count: 1309

# Emma's Dilemma

Extracts from this document...

Introduction

Emma is playing with the different arrangements of the letters in her name, here is a list of all the different arrangements: 1- emma 2- emam 3- eamm 4- amme 5- amem 6- aemm 7- mmae 8- mmea 9- mema 10- mame 11- maem 12- meam To make sure that she listed all of the possible arrangements, Emma used a systematic formula. Lets try it with the letters abcd: 1-abcd first start off by keeping the first two letters the same and then swapping the last two letters. 2-abdc Then keep the first letter where it is and swap all the second number with the third. 3-acbd Now you can swap the last two numbers and keep the first two where they are. 4-acdb Next swap the second letter with the only letter that has not been second yet which should be D, then you can swap the last two letters again. 5-adbc 6-abdc Now that you have listed all of the arrangements for the letter A you can repeat this process but each time swap the first letter for one of the others. 7-bacd 8-badc 9-bcad 10-bcda 11-bdac 12-bdca 13-cabd 14-cadb 15-cbad 16-cbda 17-cdab 18-cdba 19-dabc 20-dacb 21-dbac 22-dbca 23-dcab 24-dcba Emma then tried to find the different arrangements of her friend Lucy's name, she used the same systamatic formula. ...read more.

Middle

hcad 16- hcda 17- hdac 18- hdca 19- dcha 20- dcah 21- dhac 22- dhca 23- dach 24- dahc This name had 24 different arrangements. She then created a table. No of letters No of arrangements 3 6 4 24 5 120 She then realised that to work out the number of arrangements you would have to times the amount of letters in that name by the number of arrangements of a name with 1 less letter. So for example to work out how many arrangements a name with 6 letters had you could times 6 by 120 and you should get 720. Emma then listed the arrangements of a name with six different letters and it worked. She then continued the table. 6 720 7 5040 8 40320 9 362880 Emma thought about it for a second and realised another way of working out the number of arrangements in a name with all different letters. If the name had 6 letters then you could try the following formula: 1*2*3*4*5*6= 720 She then tried this for the others from the table and it worked. 7fig- 1*2*3*4*5*6*7= 5040 8fig- 1*2*3*4*5*6*7*8= 40320 9fig- 1*2*3*4*5*6*7*8*9= 362880 On her calculator Emma could work out this formula quickly by pressing on button, below is ...read more.

Conclusion

She divided it by two because there were 2 of the same figure. Emma then thought about how she would work out the number of arrangements for a name with more than two of the same figures or two sets of the same figure. She tried to use the same formula as for a name with 2 of the same figures. She listed some various names, which had more than one set of the same figure. Terence Ponter 13 letters 2 T's 4 E's 2 N's 2 R's She thought about the name and decided to use trial and improvement with some different methods. First she decided to enter the calculation below into her calculator. 13! = 32'432'400 (2!*4!*2!*2!) She tried this method for some other names. Chris Aust 9 letters 2 S's 9! = 181'440 2! Daniel Assiter 13 letters 2 A's 2 E's 2 I's 2 S's 13! = 389'188'800 (2!*2!*2!*2!) By looking at the results from these names, Emma was able to work out the following formula. N=number of arrangements X= number of letters A, B, C, D= figure which appears more than once in the name (each group of same letters is shown by a different letter) ...read more.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our GCSE Emma's Dilemma section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Emma's Dilemma essays

1. ## Arrangements for names.

6 X 4 (the amount of letters) gives 24. What if there were 4 letters with 2 different? Arrangements for anna: anna anan aann nana naan nnaa There are 6 arrangements for aabb. From 2 different letters to all different letters in a 4-letter word I have found a pattern of 6, 12 and 24.

2. ## Emma's Dilemma

To prove that this is correct, I will now write out all of the arrangements: SASHA ASASH HSASA SASAH ASAHS HSAAS SAHSA ASSAH HSSAA SAHAS ASSHA HAASS SASHA ASHAS HASAS Total: SASAH ASHSA HASSA 30 SSAHA AHSSA SSAAH AHSAS SSHAA AHASS SHASA AASSH SHAAS AASHS SHSAA AAHSS From these results,

1. ## Emma's Dilemma Question One: Investigate the number of different arrangements of the letters

XYXXYXY YYXXXYX XYXXYYX YYXXYXX XYXYXXY YYXYXXX XYXYXYX YYYXXXX XYXYYXX XYYXXXY XYYXXYX XYYXYXX XYYYXXX This proves that my rule is correct. Justification The reason why this rule occurs, is because there may-be the same number of letters, but any number can be used more than once.

2. ## I have been given a problem entitled 'Emma's Dilemma' and I was given the ...

of arrangements it can make, there is only one: MM EMM: EMM is a three letter word with two letters the same. There are 3 arrangements as listed below: EMM MEM MME EMMA: We have already worked out that the word Emma has 12 arrangements as listed below: EMMA EMAM

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to