document.write( "Question 742413: I' am preparing for a test and one question that will be similar to the one on the test will be “How many ways can a teacher choose two students from a group of four students?” I looked the answer up and it is six but how do you get this answer or how do you solve this problem? \n" ); document.write( "

Algebra.Com's Answer #452456 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "To explain it to you, I'll have to go into more detail than is\r\n" );
document.write( "necessary just to solve the problem:\r\n" );
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document.write( "Suppose the students are John, Charles, Susan, and Linda. \r\n" );
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document.write( "First you work the problem as though it mattered which student \r\n" );
document.write( "the teacher spoke first.  That is, we first work the problem as \r\n" );
document.write( "though if the teacher says \"I choose Susan and John\" that would \r\n" );
document.write( "be counted as a different situation from the situation in which \r\n" );
document.write( "the teacher says \"I choose John and Susan\".  Then after getting \r\n" );
document.write( "that number, we divide that number by 2 to prevent counting those\r\n" );
document.write( "as 2 separate cases.\r\n" );
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document.write( "There are 4 choices for the student the teacher calls first.  For \r\n" );
document.write( "each of those 4 choices of students the teacher calls first, there \r\n" );
document.write( "remain 3 choices for the name the teacher calls second.  So that's\r\n" );
document.write( "4×3 or 12 ways the teacher can fill in the blanks of \"I choose ____ \r\n" );
document.write( "and _____\".  Those are (I'll list them for illustration purposes \r\n" );
document.write( "but you don't have to:\r\n" );
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document.write( "1.  \"I choose John and Charles\".\r\n" );
document.write( "2.  \"I choose John and Susan\".\r\n" );
document.write( "3.  \"I choose John and Linda\".\r\n" );
document.write( "4.  \"I choose Charles and John\".\r\n" );
document.write( "5.  \"I choose Charles and Susan\".\r\n" );
document.write( "6.  \"I choose Charles and Linda\".\r\n" );
document.write( "7.  \"I choose Susan and John\".\r\n" );
document.write( "8.  \"I choose Susan and Charles\".\r\n" );
document.write( "9.  \"I choose Susan and Linda\".\r\n" );
document.write( "10.  \"I choose Linda and John\".\r\n" );
document.write( "11.  \"I choose Linda and Charles\".\r\n" );
document.write( "12.  \"I choose Linda and Susan\".\r\n" );
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document.write( "But you see in that list that number 1 is the same as number 4,\r\n" );
document.write( "Number 2 is the same as number 7, etc.,\r\n" );
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document.write( "So therefore we have to divide the number 12 by 2 to keep from\r\n" );
document.write( "counting those duplicates twice.  That in effect scratches\r\n" );
document.write( "through all the duplicates:  \r\n" );
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document.write( "1.  \"I choose John and Charles\".\r\n" );
document.write( "2.  \"I choose John and Susan\".\r\n" );
document.write( "3.  \"I choose John and Linda\".\r\n" );
document.write( "4.  \"I choose Charles and John\".\r\n" );
document.write( "5.  \"I choose Charles and Susan\".\r\n" );
document.write( "6.  \"I choose Charles and Linda\".\r\n" );
document.write( "7.  \"I choose Susan and John\".\r\n" );
document.write( "8.  \"I choose Susan and Charles\".\r\n" );
document.write( "9.  \"I choose Susan and Linda\".\r\n" );
document.write( "10.  \"I choose Linda and John\".\r\n" );
document.write( "11.  \"I choose Linda and Charles\".\r\n" );
document.write( "12.  \"I choose Linda and Susan\".  \r\n" );
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document.write( "So the answer is 12÷2 or 6\r\n" );
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document.write( "The formula is C(n,r) =  where n=4 is the\r\n" );
document.write( "number we have to choose FROM, and r=2 is the number we CHOOSE.\r\n" );
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document.write( "C(n,r) = \r\n" );
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document.write( "C(4,2) =  =  =  = 6\r\n" );
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document.write( "Edwin

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