document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31564>Question 31564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of different 5-card hands that can be dealt from a standard deck of 52 playing cards?\r<BR>\n" );
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document.write( "Find the probability that 4 kings and a queen are randomly drawn from a standard deck of 52 playing cards? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18245 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ok....52 cards:\r<BR>\n" );
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document.write( "there are 52 possible choices...Pick one <BR>\n" );
document.write( "there are now 51... Pick second<BR>\n" );
document.write( "there are now 50... pick the third<BR>\n" );
document.write( "there are now 49... pick 4th<BR>\n" );
document.write( "there are now 48... pick 5th\r<BR>\n" );
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document.write( "So, possible number of variations are: 52*51*50*49*48. However, some of these are repeated. How many are repeated?\r<BR>\n" );
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document.write( "Well, look at an easier example: Pick 2 letters from ABCDE:\r<BR>\n" );
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document.write( "AB BA CA DA EA<BR>\n" );
document.write( "AC BC CB DB EB<BR>\n" );
document.write( "AD BD CD DC EC<BR>\n" );
document.write( "AE BE CE DE ED\r<BR>\n" );
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document.write( "So from 5 choices we have 5*4 --> 20. And yet AB is the same as BA, in terms of them being playing cards...the hand is the same irrespective of having A then B dealt or B then A...the hand is still \"A and B\". Looking, there are actually only 10 different \"hands\" in this example: 20/2!. \r<BR>\n" );
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document.write( "Another example: pick 3 from the 5:<BR>\n" );
document.write( "ABC BCD CDE<BR>\n" );
document.write( "ABD BCE<BR>\n" );
document.write( "ABE BDE<BR>\n" );
document.write( "ACD<BR>\n" );
document.write( "ACE<BR>\n" );
document.write( "ADE\r<BR>\n" );
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document.write( "Here there are 10 solutions gotten from (5*4*3)/3!\r<BR>\n" );
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document.write( "So, for your question, we get 52*51*50*49*48/5!<BR>\n" );
document.write( "which is 2,598,960 different hands\r<BR>\n" );
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document.write( "This gives us that the probability of a particular hand = 1/2598960\r<BR>\n" );
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document.write( "Now P(4 kings and a queen) is actually 4 potential hands...<BR>\n" );
document.write( "4K and Q clubs or<BR>\n" );
document.write( "4K and Q diamonds or<BR>\n" );
document.write( "4K and Q hearts or<BR>\n" );
document.write( "4K and Q spades\r<BR>\n" );
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document.write( "so, P(4K and a Q) = 4*(1/2598960)<BR>\n" );
document.write( "4/2598960\r<BR>\n" );
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document.write( "As you can see, the odds are very small of this happening\r<BR>\n" );
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document.write( "jon.<BR>\n" );
document.write( " </SPAN>\n" );
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