document.write( "Question 927516: Eight plates are stacked in three piles with two piles of three plates each and one pile of
\n" ); document.write( "two plates. You are to pick up the plates one at a time following these rules:
\n" ); document.write( "1) You first choose a pile from which to pick up a plate.
\n" ); document.write( "2) You must then pick up the top plate from that pile.
\n" ); document.write( "By following these rules, in how many different orders can you pick up the eight plates? \n" ); document.write( "
Algebra.Com's Answer #563136 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let A be the 1st pile of 3 plates.\r\n" );
document.write( "Let B be the 2nd pile of 3 plates.  \r\n" );
document.write( "Let C be the pile with 2 plates.\r\n" );
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document.write( "Each time you pick up all 8 plates can be represented by \r\n" );
document.write( "a seqeunce of 8 which contains 3 A's, 3 B's and 2 C's,\r\n" );
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document.write( "For instance, the sequence of 8: \r\n" );
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document.write( "B,C,A,C,B,A,B,A represents the case where we pick up a plate from\r\n" );
document.write( "pile B, then a plate from pile C, then one from A, C, and so\r\n" );
document.write( "on until the 8th plate is picked from pile A.\r\n" );
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document.write( "In each such sequence there are C(8,3) positions for the 3 A's\r\n" );
document.write( "to go.\r\n" );
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document.write( "That leaves 5 remaining positions for the B's to go.  So there\r\n" );
document.write( "are then C(5,3) to choose positions for the B's to go.  Then the\r\n" );
document.write( "remaining 2 are where the C's go.\r\n" );
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document.write( "Answer: C(8,3)C(5,3)C(2,2) = 56*10*1 = 560 ways to pick up\r\n" );
document.write( "all the plates.\r\n" );
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document.write( "Edwin

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