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How many different 3 letter \"words\" can be made using letters of
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document.write( "Case 1: The number of 3-letter \"words\" from \"MATHEICS\" (i.e., with\r\n" );
document.write( "no letters occurring twice). \r\n" );
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document.write( "That's the permutations of 8 letters taken 3 at a time, or \r\n" );
document.write( "8P3 = 8*7*6 = 336 \"words\".\r\n" );
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document.write( "Case 2: The number containing 2 like letters.\r\n" );
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document.write( "We can choose the letter to occur twice in 3 ways {M,A,T}. \r\n" );
document.write( "For each of those choices, we can choose the third letter 7 ways.\r\n" );
document.write( "For each of those 3*7 choices we can place the third (non-\r\n" );
document.write( "repeated letter) 3 ways (1st,2nd or 3rd, e.g., {AMM,MAM,MMA} ).\r\n" );
document.write( "That's 3*7*3 = 63 \"words\".\r\n" );
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document.write( "Grand total: 336+63 = 399 \"words\".\r\n" );
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document.write( "Here is a computer generation of all 399 \"words\", 20 rows of 20 each \r\n" );
document.write( "except the last row has 1 fewer. (20x20-1 = 400-1 = 399):\r\n" );
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document.write( "AAC AAE AAH AAI AAM AAS AAT ACA ACE ACH ACI ACM ACS ACT AEA AEC AEH AEI AEM AES\r\n" );
document.write( "AET AHA AHC AHE AHI AHM AHS AHT AIA AIC AIE AIH AIM AIS AIT AMA AMC AME AMH AMI\r\n" );
document.write( "AMM AMS AMT ASA ASC ASE ASH ASI ASM AST ATA ATC ATE ATH ATI ATM ATS ATT CAA CAE\r\n" );
document.write( "CAH CAI CAM CAS CAT CEA CEH CEI CEM CES CET CHA CHE CHI CHM CHS CHT CIA CIE CIH\r\n" );
document.write( "CIM CIS CIT CMA CME CMH CMI CMM CMS CMT CSA CSE CSH CSI CSM CST CTA CTE CTH CTI\r\n" );
document.write( "CTM CTS CTT EAA EAC EAH EAI EAM EAS EAT ECA ECH ECI ECM ECS ECT EHA EHC EHI EHM\r\n" );
document.write( "EHS EHT EIA EIC EIH EIM EIS EIT EMA EMC EMH EMI EMM EMS EMT ESA ESC ESH ESI ESM\r\n" );
document.write( "EST ETA ETC ETH ETI ETM ETS ETT HAA HAC HAE HAI HAM HAS HAT HCA HCE HCI HCM HCS\r\n" );
document.write( "HCT HEA HEC HEI HEM HES HET HIA HIC HIE HIM HIS HIT HMA HMC HME HMI HMM HMS HMT\r\n" );
document.write( "HSA HSC HSE HSI HSM HST HTA HTC HTE HTI HTM HTS HTT IAA IAC IAE IAH IAM IAS IAT\r\n" );
document.write( "ICA ICE ICH ICM ICS ICT IEA IEC IEH IEM IES IET IHA IHC IHE IHM IHS IHT IMA IMC\r\n" );
document.write( "IME IMH IMM IMS IMT ISA ISC ISE ISH ISM IST ITA ITC ITE ITH ITM ITS ITT MAA MAC\r\n" );
document.write( "MAE MAH MAI MAM MAS MAT MCA MCE MCH MCI MCM MCS MCT MEA MEC MEH MEI MEM MES MET\r\n" );
document.write( "MHA MHC MHE MHI MHM MHS MHT MIA MIC MIE MIH MIM MIS MIT MMA MMC MME MMH MMI MMS\r\n" );
document.write( "MMT MSA MSC MSE MSH MSI MSM MST MTA MTC MTE MTH MTI MTM MTS MTT SAA SAC SAE SAH\r\n" );
document.write( "SAI SAM SAT SCA SCE SCH SCI SCM SCT SEA SEC SEH SEI SEM SET SHA SHC SHE SHI SHM\r\n" );
document.write( "SHT SIA SIC SIE SIH SIM SIT SMA SMC SME SMH SMI SMM SMT STA STC STE STH STI STM\r\n" );
document.write( "STT TAA TAC TAE TAH TAI TAM TAS TAT TCA TCE TCH TCI TCM TCS TCT TEA TEC TEH TEI\r\n" );
document.write( "TEM TES TET THA THC THE THI THM THS THT TIA TIC TIE TIH TIM TIS TIT TMA TMC TME\r\n" );
document.write( "TMH TMI TMM TMS TMT TSA TSC TSE TSH TSI TSM TST TTA TTC TTE TTH TTI TTM TTS\r\n" );
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document.write( "Note that some are REAL words, ACE, ACT, AHA, AIM, ASH, ATE, CAM, CAT,\r\n" );
document.write( "EAT, HAT, HEM, HIM, HIS, HIT, ICE, ITS, MAT, SAT, SEA, SET, SHE, SIT, \r\n" );
document.write( "TAM, TEA, THE, TIE, and probably some more less used words such as \r\n" );
document.write( "HIE, TIC, and CHI, ETA (Greek letters). :)\r\n" );
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document.write( "Edwin \n" );
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