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Maths Coursework 1. Investigate the number of arrangements of Dave's name......... DAVE DAEV DEAV DEVA DVAE DVEA ADEV ADVE AEDV AEVD AVED AVDE VDAE VDEA VEDA VEAD VAED VADE EVDA EVAD EDVA EDAV EAVD EADV There are 24 different arrangements for Dave's name. * For a two letter word (AT) , there are two arrangements. AT TA * For a three letter(CAT) word, there are six arrangements. CAT CTA ACT ATC TAC TCA * For a four letter word (LEAD), there are twenty-four arrangements. LEAD LEDA LAED LADE LDEA LDAE DEAL DELA DLEA DLAE DALE DAEL ADEL ADLE ALED ALDE AEDL AELD EALD EADL EDAL EDLA ELDA ELAD * For a five letter word (SOUTH), there are one hundred and twenty arrangements. SOUTH SOTUH SOHUT SOUHT SOHTU SOTHU SUOTH SUOHT SUHOT SUHTO SUTOH SUTHO STUHO STUOH STHUO STHOU STOHU STOUH SHTOU SHTUO SHUOT SHUTO SHOYU SHOUT OSUTH OSUHT OSHUT OSHTU OSTHU OSTUH OTSUH OTSHU OTHSU OTHUS OTUSH OTUHS OUTHS OUTSH OUSTH OUSHT OUHST OUHTS OHUTS OHUST OHSUT OHSTU OHTSU OHTUS UOSTH UOSHT UOHST UOHTS UOTSH UOTHS UTOHS UTOSH UTSOH UTSHO UTHOS UTHSO USTHO USTOH USOTH USOHT USHOT USHTO UHTSO UHTOS UHOTS UHOST UHSTO UHSOT THUOS THUSO THSUO THOSU THOUS TSHOU TSHUO TSUHO TSUOH TSOUH TSOHU TOSHU TOSUA TOUSH TOUHS TOHSU TOHUS TUHSO TUHOS TUSOH TUSHO TUOHS TUOSH HSOUT HSOTU HSTUO HSTOU HSUTO HSOUT HTSOU HTSUO HTUSO HTUOS HTOUS HTOSU HUOST HUOTS HUTOS HUTSO HUSTO HUSOT HOUST HOUTS HOTUS HOTSU HOSTU HOSUT The table below shows the number of arrangements for different length words. Number of letters Number of arrangements Calculation 2 2 1x2 3 6 1x2x3 4 24 1x2x3x4 5 120 1x2x3x4x5 6 720 1x2x3x4x5x6 7 5040 1x2x3x4x5x6x7 From this I have concluded that the formula n! is correct( n representing the number of letters). Therefore, to find the number of arrangements for six letter word, you would multiply the number of letters (6) by the number of arrangements of the previous number (120). This gives seven hundred and twenty arrangements. I then tried to simplify this. By doing so I found that multiplying all the numbers below the number of letters in the given word...

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