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EMMA'S DILEMMA I will now try some simple cases of rearranging letters to count the number of different combinations. TWO LETTER WORDS: AB BA CC THREE LETTER WORDS: ABC ACB BAC BCA CBA CAB ABB BAB BBA FOUR LETTER WORDS: CLUY CLYU CULY CYLU CYUL CUYL LUCY LYCU LCYU LCUY LUYC UYCL UYLC ULCY ULYC UCYL UCLY YCUL YCLU YLCU YLUC YUCL YULC AEMM AMME AMEM EMMA EAMM EMAM MEMA MEAM MMEA MMAE MAME MAEM RESULTS TABLE: NAME Number of different combinations CC 1 AB 2 ABB 3 ABC 6 EMMA 12 LUCY 24 In my table I have spotted a pattern. The pattern is when a name has two letters the same it only has half the combinations of a name with all letters different. PREDICTION: I predict that if a word has 2 of the same letters then it has half the number of combinations than a word with the same amount of letters, of which all are different. I will now test my prediction on 2, five-letter words. I will use a five-letter word with...

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