document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1056986>Question 1056986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places.\r<BR>\n" );
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document.write( "Determine the probability that all five of these cards are Spades. \r<BR>\n" );
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document.write( "Determine the probability that exactly 3 of these cards are face cards. <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 #672081 by </B><A HREF=/tutors/aboutme.mpl?userid=solve_for_x><B>solve_for_x(190)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solve_for_x><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=672081\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number of ways that a hand of 5 spades can be drawn is:\r<BR>\n" );
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document.write( "C(13, 5) * C(39, 0) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813%21%2F%285%21%2813-5%29%21%29%29+%2A+%2839%21%2F%280%21%2839-0%29%21%29%29 ALIGN=MIDDLE  ALT=\"%2813%21%2F%285%21%2813-5%29%21%29%29+%2A+%2839%21%2F%280%21%2839-0%29%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1287 * 1 = 1287 ways\r<BR>\n" );
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document.write( "The number of ways that ANY 5-card hand can be drawn from a deck of 52 cards is:\r<BR>\n" );
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document.write( "C(52, 5) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52%21+%2F+%285%21%2852-5%29%21%29 ALIGN=MIDDLE  ALT=\"52%21+%2F+%285%21%2852-5%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2598960\r<BR>\n" );
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document.write( "The probability is then:\r<BR>\n" );
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document.write( "P(5 spades) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1287%2F2598960 ALIGN=MIDDLE  ALT=\"1287%2F2598960\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.00049520 = <strong>0.0495%</strong>\r<BR>\n" );
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document.write( "For the hand with exactly 3 face cards, there are 12 face cards in the deck (3 in each suit),<BR>\n" );
document.write( "and 52 - 12 = 40 non-face cards.\r<BR>\n" );
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document.write( "The number of ways of drawing a 5-card hand with exactly 3 face cards is equal to <BR>\n" );
document.write( "the number of ways of selecting 3 out of 12 face cards, multiplied by the number of<BR>\n" );
document.write( "ways of selecting 2 of the 40 non-face cards:\r<BR>\n" );
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document.write( "C(12, 3) * C(40, 2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%21%2F%283%21%2812-3%29%21%29%29+%2A+%2840%21%2F%282%21%2840-2%29%21%29%29 ALIGN=MIDDLE  ALT=\"%2812%21%2F%283%21%2812-3%29%21%29%29+%2A+%2840%21%2F%282%21%2840-2%29%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 220 * 780 = 171600\r<BR>\n" );
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document.write( "The number of ways of drawing any 5-card hand is still 2598960 (from above)\r<BR>\n" );
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document.write( "The probability is then:\r<BR>\n" );
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document.write( "P(exactly 3 face cards) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=171600%2F2598960 ALIGN=MIDDLE  ALT=\"171600%2F2598960\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.0660264 = <strong>6.6026%</strong>\r<BR>\n" );
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