document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=819312>Question 819312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that seven playing cards are to be randomly selected from a full deck of 52.\r<BR>\n" );
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document.write( "A.  Find the probability of getting \"three of a kind\" and nothing better (i.e. three cards of the same denomination, with no more than one of any other denomination.)\r<BR>\n" );
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document.write( "B.  Find the probability of obtaining a \"flush\", ie. seven cards that are all in the same suit.\r<BR>\n" );
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document.write( "C.  Find the odds of the event described in part (b).<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #493051 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=493051\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that seven playing cards are to be randomly selected from a full deck of 52. <BR>\n" );
document.write( "A. Find the probability of getting \"three of a kind\" and nothing better (i.e. three cards of the same denomination, with no more than one of any other denomination.)<BR>\n" );
document.write( "Pick a denomination: 13 ways<BR>\n" );
document.write( "Pick 3 cards of that denomination: 4C3 = 4 ways<BR>\n" );
document.write( "Pick another denomination: 12 ways<BR>\n" );
document.write( "Pick a card of that denomination: 4 ways<BR>\n" );
document.write( "Pick a 3rd denomination: 11 ways: 11 ways<BR>\n" );
document.write( "Pick a card of that denomination: 4 ways<BR>\n" );
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document.write( "# of ways to succeed: (13*4*12*4*11*4)<BR>\n" );
document.write( "# of possible outcomes: 52C5<BR>\n" );
document.write( "Ans: [13P3*4^3]/52C5 <BR>\n" );
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document.write( "B. Find the probability of obtaining a \"flush\", ie. seven cards that are all in the same suit.<BR>\n" );
document.write( "Pick a suit: 4 ways<BR>\n" );
document.write( "Pick 7 cards from that suit: 13C7<BR>\n" );
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document.write( "Ans: (4*13C7)/52C7 = 6864/52C7 <BR>\n" );
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document.write( "C. Find the odds of the event described in part (b).<BR>\n" );
document.write( "Ans: 6864:[52C7-6864] = 6864/133777696<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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