document.write( "Question 702319: How many simple events does the sample space contain when n coins
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Algebra.Com's Answer #432916 by Edwin McCravy(20065)\"\" \"About 
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How many elements (simple events) does the sample space contain when n coins
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document.write( "Here is the sample space when 2 coins are thrown 3 times:\r\n" );
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document.write( "{(HH,HH,HH), (HH,HH,HT), (HH,HH,TH), (HH,HH,TT),\r\n" );
document.write( " (HH,HT,HH), (HH,HT,HT), (HH,HT,TH), (HH,HT,TT),\r\n" );
document.write( " (HH,TH,HH), (HH,TH,HT), (HH,TH,TH), (HH,TH,TT),\r\n" );
document.write( " (HH,TT,HH), (HH,TT,HT), (HH,TT,TH), (HH,TT,TT),\r\n" );
document.write( " (HT,HH,HH), (HT,HH,HT), (HT,HH,TH), (HT,HH,TT),\r\n" );
document.write( " (HT,HT,HH), (HT,HT,HT), (HT,HT,TH), (HT,HT,TT),\r\n" );
document.write( " (HT,TH,HH), (HT,TH,HT), (HT,TH,TH), (HT,TH,TT),\r\n" );
document.write( " (HT,TT,HH), (HT,TT,HT), (HT,TT,TH), (HT,TT,TT),\r\n" );
document.write( " (TH,HH,HH), (TH,HH,HT), (TH,HH,TH), (TH,HH,TT),\r\n" );
document.write( " (TH,HT,HH), (TH,HT,HT), (TH,HT,TH), (TH,HT,TT),\r\n" );
document.write( " (TH,TH,HH), (TH,TH,HT), (TH,TH,TH), (TH,TH,TT),\r\n" );
document.write( " (TH,TT,HH), (TH,TT,HT), (TH,TT,TH), (TH,TT,TT),\r\n" );
document.write( " (TT,HH,HH), (TT,HH,HT), (TT,HH,TH), (TT,HH,TT),\r\n" );
document.write( " (TT,HT,HH), (TT,HT,HT), (TT,HT,TH), (TT,HT,TT),\r\n" );
document.write( " (TT,TH,HH), (TT,TH,HT), (TT,TH,TH), (TT,TH,TT),\r\n" );
document.write( " (TT,TT,HH), (TT,TT,HT), (TT,TT,TH), (TT,TT,TT))\r\n" );
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document.write( "Each simple event consists of a group of 3 tosses each, and\r\n" );
document.write( "each contains 2 coin tosses, so there are \r\n" );
document.write( "2×3 or 6 places to put H or T. So there are 22×3\r\n" );
document.write( "elements in the sample space. 22×3 = 26 = 64.\r\n" );
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document.write( "Here is the sample space when 3 coins are thrown 2 times:\r\n" );
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document.write( "{(HHH,HHH),  (HHH,HHT),  (HHH,HTH),  (HHH,HTT),\r\n" );
document.write( " (HHH,THH),  (HHH,THT),  (HHH,TTH),  (HHH,TTT),\r\n" );
document.write( " (HHT,HHH),  (HHT,HHT),  (HHT,HTH),  (HHT,HTT),\r\n" );
document.write( " (HHT,THH),  (HHT,THT),  (HHT,TTH),  (HHT,TTT),\r\n" );
document.write( " (HTH,HHH),  (HTH,HHT),  (HTH,HTH),  (HTH,HTT),\r\n" );
document.write( " (HTH,THH),  (HTH,THT),  (HTH,TTH),  (HTH,TTT),\r\n" );
document.write( " (HTT,HHH),  (HTT,HHT),  (HTT,HTH),  (HTT,HTT),\r\n" );
document.write( " (HTT,THH),  (HTT,THT),  (HTT,TTH),  (HTT,TTT),\r\n" );
document.write( " (THH,HHH),  (THH,HHT),  (THH,HTH),  (THH,HTT),\r\n" );
document.write( " (THH,THH),  (THH,THT),  (THH,TTH),  (THH,TTT),\r\n" );
document.write( " (THT,HHH),  (THT,HHT),  (THT,HTH),  (THT,HTT),\r\n" );
document.write( " (THT,THH),  (THT,THT),  (THT,TTH),  (THT,TTT),\r\n" );
document.write( " (TTH,HHH),  (TTH,HHT),  (TTH,HTH),  (TTH,HTT),\r\n" );
document.write( " (TTH,THH),  (TTH,THT),  (TTH,TTH),  (TTH,TTT),\r\n" );
document.write( " (TTT,HHH),  (TTT,HHT),  (TTT,HTH),  (TTT,HTT),\r\n" );
document.write( " (TTT,THH),  (TTT,THT),  (TTT,TTH),  (TTT,TTT)}\r\n" );
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document.write( "Each simple event consists of a group of 2 tosses each, and\r\n" );
document.write( "each contains 3 coin tosses, so there are \r\n" );
document.write( "3×2 or 6 places to put H or T. So there are 23×2\r\n" );
document.write( "elements in the sample space. 22×3 = 26 = 64.\r\n" );
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document.write( "Now if we were to list the sample space when n coins are thrown m times,\r\n" );
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document.write( "Each simple event consists of a group of m tosses each, and\r\n" );
document.write( "each contains n choices of coin tosses, so there are \r\n" );
document.write( "n×m places to put H or T. So there are 2n×m\r\n" );
document.write( "elements in the sample space.\r\n" );
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document.write( "Edwin
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