document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119661>Question 1119661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places.<BR>\n" );
document.write( "a) Determine the probability that exactly 3 of these cards are Aces.<BR>\n" );
document.write( "b) Determine the probability of selecting exactly 2 Aces and exactly 2 Kings<BR>\n" );
document.write( "c) Determine the probability of selecting exactly 1 Jack. </SPAN>\n" );
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document.write( "These are all straightforward probability questions that can be answered using the \"n choose r\" concept and basic rules of probability.<br><BR>\n" );
document.write( "The number of possible hands is \"52 choose 5\":<BR>\n" );
document.write( "C(52,5) = 2598960.<br><BR>\n" );
document.write( "(a) To get exactly 3 aces, you need to choose 3 of the 4 aces and 2 of the other 48 cards.  The number of ways to do that is<BR>\n" );
document.write( "C(4,3)*C(48,2) = 6768<br><BR>\n" );
document.write( "The probability of getting exactly 3 aces is then 6768/2598960 = .0026<br><BR>\n" );
document.write( "(b) To get exactly 2 aces and 2 kings, you need to choose 2 of the 4 aces, 2 of the 4 kings, and 1 of the other 44 cards.  The number of ways to do that is<BR>\n" );
document.write( "C(4,2)*C(4,2)*C(44,1) = 1584<br><BR>\n" );
document.write( "The probability is then 1584/2598960 = .00006  (.0001, to 4 decimal places)<br><BR>\n" );
document.write( "(c) To get exactly 1 jack, you need to choose 1 of the 4 jacks and 4 of the other 48 cards.  The number of ways to do that is<BR>\n" );
document.write( "C(4,1)*C(48,4) = 778320<br><BR>\n" );
document.write( "The probability is then 778320/2598960 = .2995 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );