document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023146>Question 1023146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose we draw a four card hand from a standard 52 card deck. <BR>\n" );
document.write( "A) how many different hands contain 3 cards of the same value?\r<BR>\n" );
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document.write( "B) how many different hands contain 4 cards of the same value? </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "Suppose we draw a four card hand from a standard 52 card deck. <BR>\n" );
document.write( "A) how many different hands contain 3 cards of the same value?<BR>\n" );
document.write( "B) how many different hands contain 4 cards of the same value?<BR>\n" );
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document.write( "Solution: <BR>\n" );
document.write( "Four-card hands means that order does not count.<BR>\n" );
document.write( "There are 13 \"values\" in a deck, each in 4 different suits.<BR>\n" );
document.write( "In the following, the combination \"n choose r\" is represented by<BR>\n" );
document.write( "C(n,r)=n!/(r!(n-r)!)<BR>\n" );
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document.write( "A) 3 cards of the same value<BR>\n" );
document.write( "For each \"value\", i.e. Ace, 2, 3....10,J,Q,K, there are C(4,3)=4 ways to choose the three cards, AND (13-1)=12 different ways to choose the fourth card.<BR>\n" );
document.write( "There are thus 4*12=48 different hands that contain 3 card of the same value for each value.  Since there are 13 \"values\" per pack, so there are 13*48=624 such hands.<BR>\n" );
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document.write( "B) 4 cards of the same value.<BR>\n" );
document.write( "For each value, there is only C(4,4)=1 way to choose all four cards of the same value.  Multiplied by 13 values, there are 13 such hands. </SPAN>\n" );
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