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Emma's Dilemma  

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EMMA is investigating the amount of different arrangements of letters in her name; she does the same with her friend LUCY. LUCY has twice as many arrangements as EMMA, they are curious as to why this is and decide to investigate other names and find reasons for their answers. EMMA - emma, eamm, emam, aemm, amme, amem, meam, maem, mame, mema, mmea, mmea, LUCY - lucy, luyc, lycu, lyuc, lcyu, lcuy, ulcy, ulyc, uylc, uycl, ucly, ucyl, cluy, clyu, culy, cuyl, cyul, cylu, yluc, ylcu, yulc, yucl, yclu, ycul, Emma has 12 combinations and Lucy has 24. 1/2 of 24 = 12 so Emma has half the amount that Lucy has; this may be because Emma has 2 letters the same. I will be investigating whther this happens to other names as well. I will Investigate - * The amount of combinations for names with 2-10 letters * What happens when those names have 2 letters the same * What happens when they have 2,3,4,5 etc. letters the same * Whether 3 letters the same means 1/3 of the combinations it would have if no letters were the...

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