document.write( "Question 985313: How many words can be formed by using all the letters of the word SCHOOL so that vowels never come together?
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Algebra.Com's Answer #606135 by Edwin McCravy(20056) $\"\"$ $\"About$

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How many words can be formed by using all the letters of the word SCHOOL so that
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document.write( "First we calculate the number of distinguishable ways in which the letters of\r\n" );
document.write( "\"SCHOOL\" can be arranged without regard to whether the two Os come together or not.\r\n" );
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document.write( "If the two O's were distinguishable the number would be 6!.  But since the 2\r\n" );
document.write( "O's can be placed in 2 of the 6 positions in every arrangement, we must divide\r\n" );
document.write( "by 2!.  Thus there are 6!/2! = 360 distinguishable arrangements of \"SCHOOL\".\r\n" );
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document.write( "From that number we must subtract the number of arrangements in which the two\r\n" );
document.write( "O's come together.  This is all the arrangements of these 5 things:\r\n" );
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document.write( "S,C,H,(OO),L\r\n" );
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document.write( "which is 5!\r\n" );
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document.write( "Answer: 6!/2!-5! = 360/2-120 = 240 \r\n" );
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document.write( "Computer check:\r\n" );
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document.write( "The computer printed 24 rows of 10 each.  So 240 is the correct answer:\r\n" );
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document.write( " 1. SCHOLO SCOHLO SCOHOL SCOLHO SCOLOH SCLOHO SHCOLO SHOCLO SHOCOL SHOLCO\r\n" );
document.write( " 2. SHOLOC SHLOCO SOCHLO SOCHOL SOCLHO SOCLOH SOCOHL SOCOLH SOHCLO SOHCOL\r\n" );
document.write( " 3. SOHLCO SOHLOC SOHOCL SOHOLC SOLCHO SOLCOH SOLHCO SOLHOC SOLOCH SOLOHC\r\n" );
document.write( " 4. SLCOHO SLHOCO SLOCHO SLOCOH SLOHCO SLOHOC CSHOLO CSOHLO CSOHOL CSOLHO\r\n" );
document.write( " 5. CSOLOH CSLOHO CHSOLO CHOSLO CHOSOL CHOLSO CHOLOS CHLOSO COSHLO COSHOL\r\n" );
document.write( " 6. COSLHO COSLOH COSOHL COSOLH COHSLO COHSOL COHLSO COHLOS COHOSL COHOLS\r\n" );
document.write( " 7. COLSHO COLSOH COLHSO COLHOS COLOSH COLOHS CLSOHO CLHOSO CLOSHO CLOSOH\r\n" );
document.write( " 8. CLOHSO CLOHOS HSCOLO HSOCLO HSOCOL HSOLCO HSOLOC HSLOCO HCSOLO HCOSLO\r\n" );
document.write( " 9. HCOSOL HCOLSO HCOLOS HCLOSO HOSCLO HOSCOL HOSLCO HOSLOC HOSOCL HOSOLC\r\n" );
document.write( "10. HOCSLO HOCSOL HOCLSO HOCLOS HOCOSL HOCOLS HOLSCO HOLSOC HOLCSO HOLCOS\r\n" );
document.write( "11. HOLOSC HOLOCS HLSOCO HLCOSO HLOSCO HLOSOC HLOCSO HLOCOS OSCHLO OSCHOL\r\n" );
document.write( "12. OSCLHO OSCLOH OSCOHL OSCOLH OSHCLO OSHCOL OSHLCO OSHLOC OSHOCL OSHOLC\r\n" );
document.write( "13. OSLCHO OSLCOH OSLHCO OSLHOC OSLOCH OSLOHC OSOCHL OSOCLH OSOHCL OSOHLC\r\n" );
document.write( "14. OSOLCH OSOLHC OCSHLO OCSHOL OCSLHO OCSLOH OCSOHL OCSOLH OCHSLO OCHSOL\r\n" );
document.write( "15. OCHLSO OCHLOS OCHOSL OCHOLS OCLSHO OCLSOH OCLHSO OCLHOS OCLOSH OCLOHS\r\n" );
document.write( "16. OCOSHL OCOSLH OCOHSL OCOHLS OCOLSH OCOLHS OHSCLO OHSCOL OHSLCO OHSLOC\r\n" );
document.write( "17. OHSOCL OHSOLC OHCSLO OHCSOL OHCLSO OHCLOS OHCOSL OHCOLS OHLSCO OHLSOC\r\n" );
document.write( "18. OHLCSO OHLCOS OHLOSC OHLOCS OHOSCL OHOSLC OHOCSL OHOCLS OHOLSC OHOLCS\r\n" );
document.write( "19. OLSCHO OLSCOH OLSHCO OLSHOC OLSOCH OLSOHC OLCSHO OLCSOH OLCHSO OLCHOS\r\n" );
document.write( "20. OLCOSH OLCOHS OLHSCO OLHSOC OLHCSO OLHCOS OLHOSC OLHOCS OLOSCH OLOSHC\r\n" );
document.write( "21. OLOCSH OLOCHS OLOHSC OLOHCS LSCOHO LSHOCO LSOCHO LSOCOH LSOHCO LSOHOC\r\n" );
document.write( "22. LCSOHO LCHOSO LCOSHO LCOSOH LCOHSO LCOHOS LHSOCO LHCOSO LHOSCO LHOSOC\r\n" );
document.write( "23. LHOCSO LHOCOS LOSCHO LOSCOH LOSHCO LOSHOC LOSOCH LOSOHC LOCSHO LOCSOH\r\n" );
document.write( "24. LOCHSO LOCHOS LOCOSH LOCOHS LOHSCO LOHSOC LOHCSO LOHCOS LOHOSC LOHOCS\r\n" );
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document.write( "Edwin

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