document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31456>Question 31456</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you remove all face cards from a standard deck of cards, what is the probability that you will draw a full house in a 5 card hand? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20887 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=20887\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> After taking out those cards you have a deck with 40 cards <BR>\n" );
document.write( "There are 10 different cards.<BR>\n" );
document.write( "To figure the probability:<BR>\n" );
document.write( "pick a card type:   10 ways<BR>\n" );
document.write( "Now pick 3 of the 4 cards of that type: 4C3=4 ways<BR>\n" );
document.write( "Pick another card type: 9 ways<BR>\n" );
document.write( "Now pick 2 of the 4 card of that type: 4C2=6 ways<BR>\n" );
document.write( "So, number of ways to succeed is 10*4*9*6=2160\r<BR>\n" );
document.write( "\n" );
document.write( "Now figure the total number of 5 card hands in a deck of 40 cards:<BR>\n" );
document.write( "40C5= 658008 different hands<BR>\n" );
document.write( "Prob of a full house with the special deck = 2160/658008=0.00328...<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );