document.write( "Question 935198: In how many ways we can a pack of 52 Playing cards be divided in 4 sets three of them having 17 Cards each and the fourth just one card ? \n" ); document.write( "

Algebra.Com's Answer #568350 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "We will first get the number of 4 sets placed in a certain order, \r\n" );
document.write( "and then we will \"unorder\" them:\r\n" );
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document.write( "To start with we will assume we are to place the set of 1 on the far left,\r\n" );
document.write( "a set of 17 in the left middle, one set of 17 in the right middle, and \r\n" );
document.write( "a set of 17 on the far right.\r\n" );
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document.write( "We can choose the far left set in 52C1 = 52 ways, leaving 51 cards.\r\n" );
document.write( "We can choose the set in the middle left in C(51,17) ways, leaving 34 cards.\r\n" );
document.write( "We can choose the set on the middle right in C(34,17) ways, leaving 17 cards.\r\n" );
document.write( "Those 17 make up the set on the far right\r\n" );
document.write( "So that would be 52*C(51,17)*C(34,17)*1\r\n" );
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document.write( "We're not done.  There are 4! ways any group of four sets can be ordered, \r\n" );
document.write( "so we must divide by 4! to unorder them. \r\n" );
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document.write( "Answer = \r\n" );
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document.write( "Edwin

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