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• Level: GCSE
• Subject: Maths
• Word count: 1682

# permutations &amp; combinations

Extracts from this document...

Introduction

Sushant Goel                                           Maths Coursework                               Form: 10D

Candidate no: 3147

Centre no: 91036

## Plan

In this coursework, I will be dealing with an unfamiliar task. I have to get around different words and find alternative variations for them. I must try to get different letter words, so that I can apply my knowledge and understanding to a broader scope. I have to use a range of mathematical formulas and use different mathematical techniques to explain this formula and how I got there. In the end I have to give all my mathematical formulas and give a conclusion on what I have discovered.

I can start off by finding out alternatives for some simple four-letter words.

## LUCY- Different arrangements for this word:

1. UCLY
2. UCYL
3. UYLC
4. UYCL
5. ULYC
6. ULCY
7. CYUL
8. CYLU
9. CULY
10. CULY
11. CLUY
12. CLYU
13. YCUL
14. YLCU
15. YULC
16. YCLU
17. YUCL
18. YLUC
19. LUCY
20. LYCU
21. LCUY
22. LCYU
23. LYUC
24. LUYC

These were 24 different arrangements for a four-letter word, with no similar letters.

Middle

SETAMSEMTASEMATSMEATSMETASMATESMAETSMTEASMTAESAMTESAMETSAETMSAEMTSATEMSATMESEATMSEAMTSEMTASEMATSETMASETAMSTAMESTAEMSTEMASTEAMSTMAESTMEA

We have investigated the three, four and five letter words. From this we can deduce the different variations for different letter words.

Now we can move onto investigating four and five letter-words with similar letters.

EMMA- This is a four-letter word with two same letters.

1. EMMA
2. EMAM
3. EAMM
4. MEMA
5. MAME
6. MMEA
7. MMAE
8. AMME
9. AMEM
10. AEMM
11. MAEM
12. MEAM

EM1M2A - This is the same spelling as the one above, however the two M’s have been given numbers.

1. EM1M2A
2. EM2M1A
3. EAM2M1
4. EAM1M2
5. EM1AM2
6. EM2AM1
7. AEM1M2
8. AEM2M1
9. A M2EM1
10. A M1EM2
11. A M2M1E
12. AE M1M2
13. M2AEM1
14. M2EAM1
15. M2 M1 AE
16. M2 M1 E A
17. M2 EM1A
18. M2A EM1
19. M1M2A E
20. M1M2 E A
21. M1 A M2 E
22. M1 E M2A
23. M1 A E M2
24. M1 E A M2

Both EM1M2A andEMMA have the same spelling except for the subscripts. However the one without the subscripts has 12 variations while the one with the subscripts has 24.

Conclusion

EVALUATION

While discovering the formula, I went through many formulas, which were wrong. I’m going to state the formulas and show how I proved them wrong. While discovering the formula for letters with two letters, which are repeated, I thought we add the factorials in the denominator instead of multiplying it. However this was proved wrong when I tried this word:

PPPQQ

1. PPPQQ
2. PPQQP
3. PQQPP
4. PQPPQ
5. PQPQP
6. PPQPP
7. QQPPP
8. QPPPQ
9. QPPQP
10. QPQPP

If the denominators were being added, I would have had 15 variations.

I also started on finding a few big words variations but decided not to carry on, e.g. Mississippi. I realized it was a tedious process and there was no point in finding it out.

These are a few other words for which I calculated variations:

 Word No of variations PPQRS 60 CREEK 60 AABDDE 180 DUCK 24

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

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