Emma’s Dilemma We are investigating the number of different arrangements of letters.Firstly we arrange Emma’s name…EAMMEMAM MEMA MEAMMMEAMMAEMAEMMAMEAMMEAEMMAMEMEMMAThere are 12 different arrangements for the name Emma. Note that there are four letters in total and three different letters.Next I arranged Lucy…LucyUlcy UcylCuylYculLuycUclyCyulYlucYlucLycu UyclCulyYuclLcuyUlycCyluYcluLcyuUylcClyuYlcuThere 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 example for the amount of arrangements, what would happen?Arrangements for aabb…aabbbaabbabaabababbabbaaThere are six different arrangements for the letters aabb as the table shows. From Emma with two different letters to Lucy with all different letters I have found a pattern for the amount of arrangements (6, 12, 24). It is easier for me to convey more difficult arrangements through tables so I will do a table with more letters in the it, and try to look for an explanation for the different amount of arrangements. I will start with a five-letter word. I have previously found that with a four letter word with all different letters there are 24 separate arrangements and that there were six ways of starting the arrangements i.e. start with an L first then a U and so on and so on. For the sake of argument I have added a Q to the front of Lucy to make a five letters word with
