document.write( "Question 1187855: 1) We are creating a new card game with a new deck. Unlike the normal deck that
\n" ); document.write( "has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and
\n" ); document.write( "clubs), our deck will be made up of the following.\r
\n" ); document.write( "\n" ); document.write( "Each card will have:
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\n" ); document.write( "ii) One of 9 different suits.\r
\n" ); document.write( "\n" ); document.write( "Hence, there are 144 cards in the deck with 16 ranks for each of the 9 different
\n" ); document.write( "suits, and none of the cards will be face cards! So, a card rank 11 would just
\n" ); document.write( "have an 11 on it. Hence, there is no discussion of \"royal\" anything since there
\n" ); document.write( "won't be any cards that are \"royalty\" like King or Queen, and no face cards! \r
\n" ); document.write( "\n" ); document.write( "The game is played by dealing each player 5 cards from the deck. Our goal is to
\n" ); document.write( "determine which hands would beat other hands using probability. Obviously the
\n" ); document.write( "hands that are harder to get (i.e. are more rare) should beat hands that are
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\n" ); document.write( "b)How many different ways are there to get exactly 1 pair (i.e. 2 cards with the same rank)?
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Algebra.Com's Answer #819125 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "b)How many different ways are there to get exactly 1 pair (i.e. 2 cards with the\r\n" );
document.write( "same rank)?\r\n" );
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document.write( "To get one pair, we first:\r\n" );
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document.write( "Choose the 1 rank.  That's 16 ranks choose 1, 16C1=16 ways.\r\n" );
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document.write( "Then we choose the 2 suits.  That's 9 suits choose 2, 9C2=36 ways.\r\n" );
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document.write( "We choose the ranks of the other three cards different from the 1 rank that the\r\n" );
document.write( "pair has, and also different from each other, so there will not be another pair:\r\n" );
document.write( "That's 15 other ranks choose 3, 15C3 = 455 ways.\r\n" );
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document.write( "We choose the suit for the card of the other 3 with the lowest rank 9 ways.\r\n" );
document.write( "We choose the suit for the card of the other 3 with the middle rank 9 ways.\r\n" );
document.write( "We choose the suit for the card of the other 3 with the highest rank 9 ways.\r\n" );
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document.write( "That's (16C1)(9C2)(9)(9)(9) = (16)(36)(9)(9)(9) = 419904\r\n" );
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document.write( "So, the number of ways of getting exactly 1 pair is 419904 ways. \r\n" );
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document.write( "The number of ways to get any 5 cards is 144C5 = 481008528\r\n" );
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document.write( "So the probability is 419904 out of 481008528 or 419904/481008528 which\r\n" );
document.write( "reduces to 2916/3340337 or 0.0008730, to 7 decimal places.\r\n" );
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document.write( "Edwin
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