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# GCSE Maths Coursework : Emma&amp;#146;s Dilemma

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Introduction

GCSE Maths Coursework : Emma's Dilemma I tried to find as many possible arrangements of letters from the name Emma as I could and found 12 different combinations (see separate sheet.) I did the same with the name Lucy and got 24 different combinations (see separate sheet.) I did this systematically to try to avoid missing any combinations and to make it easier to spot any patterns i.e. ...read more.

Middle

With just one letter I got one combination: So 1l = 1c With two letters I got two combinations: So 2l = 2c With three letters I got six combinations: So 3l = 6c And with four letters I got twenty four combinations: So 4l = 24c From this I found that the number of different combinations (c ) ...read more.

Conclusion

that if a letter was repeated twice the number of possible combinations were halved and if three letters were the same it was divided by 6. This means that the formula for letters the same must be the formula for the number of combinations divided by number of letters the same factorial. So the formula for the number of different combinations is: - Number of Letters Factorial Number of Letters the same Factorial David Thomas 10Mk 03/08/2003 ...read more.

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