document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026409>Question 1026409</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen from the deck.\r<BR>\n" );
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document.write( "How many hands contain 4 kings? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641688 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=641688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you draw 5 cards.<BR>\n" );
document.write( "the probability that the first card will be a king is 4/52.<BR>\n" );
document.write( "the probability that the second card will be a king is 3/51.<BR>\n" );
document.write( "the probability that the third card will be a king is 2/50.<BR>\n" );
document.write( "the probability that the fourth card will be a king is 1/49.<BR>\n" );
document.write( "the probability that the fifth card will not be a king is 48/48.\r<BR>\n" );
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document.write( "this can occur 5c4 possible ways = 5 possible ways.\r<BR>\n" );
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document.write( "the probability is therefore 5 * 4 * 3 * 2 * 1 * 48 / (52 * 51 * 50 * 49 * 48).\r<BR>\n" );
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document.write( "this probability is equal to .00001846892603.\r<BR>\n" );
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document.write( "this means that, for every 54145 times you draw a hand of 5 cards from a full deck of 52 cards, you will get 1 hand that contains 4 kinds, on the average.\r<BR>\n" );
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document.write( "what does on the average mean?\r<BR>\n" );
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document.write( "it means that each set of 54145 times you draw, the number of hands won't be exactly 1 time for each set, but the overall average will be 1 or very close to it.\r<BR>\n" );
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document.write( "a small example:\r<BR>\n" );
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document.write( "first set of 54145 gets you 3 sets of hands with 4 kings.<BR>\n" );
document.write( "second set of 54145 gets you 0 sets of hands with 4 kings.<BR>\n" );
document.write( "third set of 54145 gets you 0 sets of hands with 4 kings.\r<BR>\n" );
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document.write( "the average is 3/3 = 1 hand with 4 kings in it for every 54145 times that you draw a hand of 5 cards.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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