document.write( "Question 768429: It is hard to understand where to use permutation and where to use combination. I need an answer w/ examples.
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Algebra.Com's Answer #468429 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "A Combination is just Choosing without positioning in any certain order.\r\n" );
document.write( "A Permutation is Positioning in a certain order after choosing.\r\n" );
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document.write( "If we have 5 things, {A,B,C,D,E}, we can Choose 3 in these 10 ways:\r\n" );
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document.write( "{A,B,C}. {A,B,D}, {A,B,E}, {A,C,D}, {A,C,E}, \r\n" );
document.write( "{A,D,E}, {B,C,D}, {B,C,E}, {B,D,E}, {C,D,E}\r\n" );
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document.write( "IT's 10 ways because C(5,3} =  =  = 10\r\n" );
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document.write( "But each of those Combinations can be Positioned in 6 orders:\r\n" );
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document.write( "{A,B,C} can be Positioned in these 6 ways: ABC, ACB, BAC, BCA, CAB, CBA\r\n" );
document.write( "{A,B,D} can be Positioned in these 6 ways: ABD, ADB, BAD, BDA, DAB, DBA\r\n" );
document.write( "{A,B,E} can be Positioned in these 6 ways: ABE, ACE, BAE, BEA, EAB, EBA\r\n" );
document.write( "{A,C,D} can be Positioned in these 6 ways: ACD, ADC, CAD, CDA, DAC, DCA\r\n" );
document.write( "{A,C,E} can be Positioned in these 6 ways: ACE, AEC, CAE, CEA, EAC, ECA\r\n" );
document.write( "{A,D,E} can be Positioned in these 6 ways: ADE, AED, DAE, DEA, EAD, EDA\r\n" );
document.write( "{B,C,D} can be Positioned in these 6 ways: BCD, BDC, CBD, CDB, DBC, DCB\r\n" );
document.write( "{B,C,E} can be Positioned in these 6 ways: BCE, BEC, CBE, CEB, EBC, ECB\r\n" );
document.write( "{B,D,E} can be Positioned in these 6 ways: BDE, BED, DBE, DEB, EBD, EDB\r\n" );
document.write( "{C,D,E} can be Positioned in these 6 ways: CDE, CED, DCE, DEC, ECD, EDC\r\n" );
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document.write( "So there are 6·10 or 60 Permutations of 5 things taken 3 ar a time.\r\n" );
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document.write( "P(5,3) = 5·4·3 = 60\r\n" );
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document.write( "P(n,r) = C(n,r)·r!\r\n" );
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document.write( "\"COMBINATION\" starts with a C and \"CHOOSE\" starts with a C.\r\n" );
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document.write( "\"PERMUTATION\" starts with a P and \"POSITION\" starts with a P.\r\n" );
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document.write( "Actually in both cases you choose, but with Permutation you Position\r\n" );
document.write( "each combination in all the possible orders.\r\n" );
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document.write( "Edwin

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