document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=460207>Question 460207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> its a word problem .. if out of a deck i use 20 cards ... 5 suits and 4 of each card.. what is the propability that i will chose 4 cards in the exact order as 4 random generated cards\r<BR>\n" );
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document.write( "and is the propability greater than if i use 5 cards of 4 suits ? is it less than or is it equal to\r<BR>\n" );
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document.write( "also this is to neither homework or test . i am trying to make a board game </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #315655 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20062)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=315655\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability would be less if the randomly generated sequence<BR>\n" );
document.write( "of ranks coutains duplications such as 2,1,2,3.  So I will assume<BR>\n" );
document.write( "the randomly generated sequence are 4 different ranks. <BR>\n" );
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document.write( "Suppose the randomly generated sequence is 3,4,1,2 and you use 4 ranks<BR>\n" );
document.write( "and 5 suits:<BR>\n" );
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document.write( "There are 5 3s and 20 cards, so you will pick a 3 first 5/20ths or 1/4 of the<BR>\n" );
document.write( "time.<BR>\n" );
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document.write( "Now of those 1/4ths of the times when we successfully pick the 3 first:<BR>\n" );
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document.write( "There are 5 4s and 19 cards, so you will pick a 4 second 5/19ths<BR>\n" );
document.write( "of the time.<BR>\n" );
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document.write( "So the probability of successfully picking a 3 first and a 4 second is<BR>\n" );
document.write( "5/19ths of 1/4th of the time or 5/76ths of the time<BR>\n" );
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document.write( "Now of those 5/76ths of the time when we successfully pick the 3 first<BR>\n" );
document.write( "and the 4 second:<BR>\n" );
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document.write( "There are 5 1's and 18 cards, so you will pick a 1 third 5/18ths of <BR>\n" );
document.write( "the time.<BR>\n" );
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document.write( "So the probability of successfully picking a 3 first, a 4 second, and a<BR>\n" );
document.write( "1 third is 5/18ths of 5/76ths of the time or 25/1368ths of the time<BR>\n" );
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document.write( "Now of those 25/1368ths of the time when we successfully pick the 3 first,<BR>\n" );
document.write( "the 4 second, and the 1 third:<BR>\n" );
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document.write( "There are 5 2's and 17 cards, so you will pick a 2 fourth 5/17ths of <BR>\n" );
document.write( "the time.<BR>\n" );
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document.write( "So the probability of successfully picking a 3 first, a 4 second, a<BR>\n" );
document.write( "1 third and a 2 fourth is 5/17ths of 25/1368ths of the time or 125/23256ths of the time.<BR>\n" );
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document.write( "That works out to a probability of about .005 or only 1 chance in 200.<BR>\n" );
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document.write( "Now suppose you use 5 ranks of 4 suits.<BR>\n" );
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document.write( "Suppose the randomly generated sequence is 3,4,1,2<BR>\n" );
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document.write( "There are 4 3s and 20 cards, so you will pick a 3 first 4/20ths or 1/5 of the<BR>\n" );
document.write( "time.<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Now of those 1/5ths of the time when we successfully pick the 3 first:<BR>\n" );
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document.write( "There are 4 4s and 19 cards, so you will pick a 4 second 4/19ths<BR>\n" );
document.write( "of the time.<BR>\n" );
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document.write( "So the probability of successfully picking a 3 first and a 4 second is<BR>\n" );
document.write( "4/19ths of 1/5th of the time or 4/95ths of the time<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Now of those 4/95ths of the time when we successfully pick the 3 first<BR>\n" );
document.write( "and the 4 second:<BR>\n" );
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document.write( "There are 4 1's and 18 cards, so you will pick a 1 third 4/18ths or 2/9ths<BR>\n" );
document.write( "of the time.<BR>\n" );
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document.write( "So the probability of successfully picking a 3 first, a 4 second, and a<BR>\n" );
document.write( "1 third is 2/9ths of 4/95ths of the time or 8/855ths of the time<BR>\n" );
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document.write( "Now of those 8/855ths of the time when we successfully pick the 3 first,<BR>\n" );
document.write( "the 4 second, and the 1 third:<BR>\n" );
document.write( "`<BR>\n" );
document.write( "There are 4 2's and 17 cards, so you will pick a 2 fourth 4/17ths of <BR>\n" );
document.write( "the time.<BR>\n" );
document.write( "`<BR>\n" );
document.write( "So the probability of successfully picking a 3 first, a 4 second, a<BR>\n" );
document.write( "1 third and a 2 fourth is 4/17ths of 8/855ths of the time or 32/14535ths of the time.<BR>\n" );
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document.write( "That works out to a probability of about .002 or only 1 chance in 500.<BR>\n" );
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document.write( "So the probability is higher if you use four ranks and 5 suits, but<BR>\n" );
document.write( "either way, the probability of succeding is very low, and even lower <BR>\n" );
document.write( "if you allow repetitions in the randomly selected sequence.<BR>\n" );
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document.write( "Edwin\r<BR>\n" );
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document.write( " </SPAN>\n" );
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