document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138507>Question 1138507</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you are dealt 3 cards from a shuffled deck of 52 cards, find the probability of getting one queen and two kings. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756422 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756422\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe it will be 4c2 * 4c1 / 52c3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the number of ways you can get 2 kings from 4 kings times the number of ways you can get 1 queen out of 4 queens divided by the number of ways you can get any 3 cards out of 52 cards.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4c3 = 4! / (2! * 2!) = 6<BR>\n" );
document.write( "4c1 = 4! / (1! * 3!) = 4<BR>\n" );
document.write( "52c3 = 52! / (3! * 49!) = 22100\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability is therefore 24 / 22100 = .0010859729.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can do it another way.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to get 2 kings and one queen out of deck of 52 cards give you 3 possibilities.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they are KKQ, KQK, and QKK.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that is draws 1, 2 and 3 in that order.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can draw a king on the first draw and a king on the second draw and a queen on the third draw, or you can draw a kind on the first draw and a queen on the second draw and a king on the third draw, or you can draw a queen on the first draw and a king on the second draw and a king on the third draw.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is all without replacement, so the probability changes each draw.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for KKQ, the probaiblity is 4/52 * 3/51 * 4/50.<BR>\n" );
document.write( "for KQK, the probability is 4/52 * 4/51 * 3/50.<BR>\n" );
document.write( "for QKK, the probability is 4/52 * 4/51 * 3/50.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "each oone of these probabilties is the same, so the total probability would be 3 * (4 * 3 * 4) / (52 * 51 * 50) = = .0010859729, the same as we got using the other method.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i believe that's your answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "note that ncx is equal to n! / (x! * (n-x)!).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when n = 4 and x = 2, that becomes 4! / (2! * 2!).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when n = 4 and x = 1, that becomes 4! / (1! * 3!).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when n = 52 and x = 3, that becomes 52! / (3! * 49!).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ncx can also be written as c(n,x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they mean the same thing.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );