document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126830>Question 1126830</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you have a deck of 52 playing cards (no jokers)<BR>\n" );
document.write( "A. How many five-card hands containing exactly three aces are possible?<BR>\n" );
document.write( "B. How many five-card hands containing exactly three of a kind are possible? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743313 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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/cgi-bin/show-face.mpl?user=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743313\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A.   C(4,3)*C(48,2) =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284%21%2F%283%21%2A1%21%29%29+%2A+%2848%21%2F%2846%21%2A2%21%29%29+=+4%2A1128+=+highlight%28+4512+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "B.   C(4,3)*C(48,2)*C(13,1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+58656+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+58656+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As \"three of a kind\" is a specific type of poker hand,  I should mention this answer includes full-houses  (where the non-triplicate cards match in rank).<br>\r<BR>\n" );
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document.write( "To exclude full-houses, note that there are  C(13,1)*C(4,3)*C(12,1)*C(4,2) = 3744 of them, so you would have 58656-3744 true \"three of kind\" poker hands.   \r<BR>\n" );
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