document.write( "Question 720627: In How Many Ways 50 things Can Be divided In 5 sets,such That 3 sets Contain 12 things each and the remaining 2 sets contain 7 things each? \n" ); document.write( "

Algebra.Com's Answer #441914 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "First let's find the number of ways we can create the sets that contain 12\r\n" );
document.write( "things each.  Suppose the sets A, B, and C contain 12 things each\r\n" );
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document.write( "We can fill set A in C(50,12) waye, set B in C(38,12) ways and set C(26,12).\r\n" );
document.write( "That's C(50,12)·C(38,12)·C(26,12) ways.  However we do not want to count\r\n" );
document.write( "separately any two cases say, Case 1 and Case 2, where in Case 1, set A is \r\n" );
document.write( "identical with set C of Case 2, set B is identical with set A of case 2, and\r\n" );
document.write( "set C is identical with set B of Case 2.  So to eliminate those duplicate\r\n" );
document.write( "cases we must divide by 3!\r\n" );
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document.write( "So the number of ways to create the 3 sets of 12 is \r\n" );
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document.write( "For each of those ways of creating the sets of 12, we can create the\r\n" );
document.write( "2 sets of 7 using the same reasoning  in  \r\n" );
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document.write( "So the answer is\r\n" );
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document.write( "   \r\n" );
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document.write( "or\r\n" );
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document.write( "or about 9.8×10²⁹\r\n" );
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document.write( "Edwin

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