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Emma's Dilemma We are investigating the number of different arrangements of letters. Firstly we arrange Emma's name... EAMM EMAM MEMA MEAM MMEA MMAE MAEM MAME AMME AEMM AMEM EMMA There are 12 different arrangements for the name Emma. Note that there are four letters in total and three different letters. Next I arranged Lucy... Lucy Ulcy Ucyl Cuyl Ycul Luyc Ucly Cyul Yluc Yluc Lycu Uycl Culy Yucl Lcuy Ulyc Cylu Yclu Lcyu Uylc Clyu Ylcu There are 24 different possibilities in this arrangement of the name Lucy with four letters that are all different. Twice as many as before in Emma's name which had four letters but three different letters. In the name Lucy I noticed that there were six possibilities beginning with a different letter each time. For example in the name Lucy there were six arrangements starting with L six starting with U six starting with C and six starting with Y. Therefore I found that 6 times the amount of letters (in this case 4) equaled the amount of different arrangements for the name. If we take aabb as a further...

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