document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206213>Question 1206213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five cards are selected from a 52-card deck for a poker hand.<BR>\n" );
document.write( "(a) How many simple events are in the sample space?<BR>\n" );
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document.write( " simple events\r<BR>\n" );
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document.write( "(b) A royal flush is a hand that contains the A, K, Q, J, and 10, all in the same suit. How many ways are there to get a royal flush?<BR>\n" );
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document.write( "(c) What is the probability of being dealt a royal flush? (Enter your probability as a fraction.) </SPAN>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "(a) <font color=red size=4>2,598,960</font><BR>\n" );
document.write( "(b) <font color=red size=4>4</font><BR>\n" );
document.write( "(c) <font color=red size=4>1/649740</font>\r<BR>\n" );
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document.write( "Explanation for part (a)\r<BR>\n" );
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document.write( "There are 52 ways to pick the first card. Then 51 choices for the next card, 50 for the next, and so on. <BR>\n" );
document.write( "We keep this countdown going until five cards are selected.<BR>\n" );
document.write( "52*51*50*49*48 = 311,875,200<BR>\n" );
document.write( "That is the number of permutations and would be the answer if order mattered. \r<BR>\n" );
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document.write( "But order does NOT matter with a poker hand. <BR>\n" );
document.write( "We must divide by 5! = 5*4*3*2*1 = 120 to get 311875200/120 = <font color=red>2,598,960</font> which is the final answer to part (a). This value is roughly 2.6 million.\r<BR>\n" );
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document.write( "Here's another way to reach that value.<BR>\n" );
document.write( "Use the nCr combination formula with n = 52 and r = 5.<BR>\n" );
document.write( "n C r = (n!)/(r!(n-r)!)<BR>\n" );
document.write( "52 C 5 = (52!)/(5!*(52-5)!)<BR>\n" );
document.write( "52 C 5 = (52!)/(5!*47!)<BR>\n" );
document.write( "52 C 5 = (52*51*50*49*48*47!)/(5!*47!)<BR>\n" );
document.write( "52 C 5 = (52*51*50*49*48)/(5!)<BR>\n" );
document.write( "52 C 5 = (52*51*50*49*48)/(5*4*3*2*1)<BR>\n" );
document.write( "52 C 5 = (311,875,200)/120<BR>\n" );
document.write( "52 C 5 = <font color=red>2,598,960</font>\r<BR>\n" );
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document.write( "Explanation for part (b)\r<BR>\n" );
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document.write( "There is only one way to get a royal flush for any particular suit.<BR>\n" );
document.write( "Since there are 4 suits, that yields 4 royal flushes possible.\r<BR>\n" );
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document.write( "Explanation for part (c)\r<BR>\n" );
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document.write( "Divide the results of (b) over (a)<BR>\n" );
document.write( "4/2598960 = <font color=red>1/649740</font><BR>\n" );
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