document.write( "Question 849751: in how many different ways can two students be selected from among a group of five students? How does this compare with the number of way that three students could be selected from the same group of five students? \n" ); document.write( "

Algebra.Com's Answer #512009 by Edwin McCravy(20054) $\"\"$ $\"About$

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in how many different ways can two students be selected from among a group of five students?
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C(5,2) = 10\r\n" );
document.write( "If the students are {A,B,C,D,E}, those 10 ways are\r\n" );
document.write( "{A,B}, {A,C}, {A,D}, {A,E}, {B,C}, {B,D}, {B,E}, {C,D}, {C,E}, {D,E}\r\n" );
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How does this compare with the number of way that three students could be selected from the same group of five students?

C(5,3) = 10\r\n" );
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document.write( "They are the same and the reason they are is\r\n" );
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document.write( "1. every time you pick 2 student from the 5 you are automatically picking 3 students to leave behind. \r\n" );
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document.write( "and vice-versa,\r\n" );
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document.write( "2. every time you pick 3 student from the 5 you are automatically picking 2 students to leave behind.\r\n" );
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document.write( "So they have to be the same.\r\n" );
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document.write( "If the students are {A,B,C,D,E}, those 10 ways are\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( "-------------------------------------------------\r\n" );
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document.write( "So in general, C(n,r) = C(n,n-r)\r\n" );
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document.write( "Edwin

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