Emma's Dilemma

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Emma's Dilemma The Problem: Emma is playing with arrangements of the letters of her name. One arrangement is EMMA A different arrangement is MEAM Another arrangement is AEMM Experiment: ----------- For my investigation I have been asked to work out the number of different arrangements of the letters from the name Emma. ---------------------------------------------------------------- EMMA AMEM EMAM AMME --------- EAMM MEMA MMEA MMAE MAME MEAM MAEM AEMM I have found out that when the letter "E" is at the front of the name Emma, then there are three different combinations. The same rule applies when the letter "A" is at the front of the name Emma. There is an exception though, when the letter "M" is at the front of the name Emma then there are six different combinations. Overall there are 12 different combinations for the name Emma. For the second part of my investigation I have been asked to work out the number of different arrangements of letters from the name Lucy. LUCY UYCL YCLU LCUY UYLC YULC LCYU CULY YLCU LYCU CUYL YLUC LYUC CLYU LUYC CLUY ULCY CYLU UCLY CYUL UCYL YUCL ULYC YCUL From this second experiment I have found out that when the letter "L" is at the front of the name Lucy then there are six different combinations. The same rule applies to the letters "U", "C" and "Y" in the name Lucy. Overall there are 24 different combinations for the name Lucy From the first two experiments I have noticed that the name Emma has half the number of combinations when compared with the name Lucy. This maybe because of the repeated letter "M" in the name Emma. To find out whether or not this is true I will investigate a 5-letter word with a repeated letter in it and a 5-letter word with all different letters

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