document.write( "Question 1006882: Six stand up comics, A,B,C,D,E and F are to perform on a single evening at a comedy club. The order of performance is determined by random selection. Find the probability that
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Algebra.Com's Answer #623106 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Six stand up comics, A,B,C,D,E and F are to perform on a single
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document.write( "With no restrictions 6 comedians can perform in 6! = 720 ways. This\r\n" );
document.write( "will be the denominators of each of the probabilities. \r\n" );
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\n" ); document.write( "Find the probability that\r
\n" ); document.write( "\n" ); document.write( "A.Comic C will perform first
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document.write( "C _ _ _ _ _\r\n" );
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document.write( "We can fill the 5 blanks with the 5 letters B,C,D,E,F in\r\n" );
document.write( "5! = 120 ways\r\n" );
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document.write( "The probability of that is 120 ways out of 720 or 120/720 or 1/6.\r\n" );
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document.write( "[This could also be reasoned by saying each of the 6 has an equal \r\n" );
document.write( "chance of performing first, which give us 1/6 immediately]\r\n" );
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\n" ); document.write( "B. Comic B will perform last and Comic F will perform third
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document.write( "_ _ F _ _ B\r\n" );
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document.write( "We can fill the 4 blanks with the 4 letters A,C,D,E in\r\n" );
document.write( "4! = 24 ways.\r\n" );
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document.write( "The probability of that is 24 ways out of 720 or 24/720 or 1/30.\r\n" );
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\n" ); document.write( "C. The comedians will perform in the following order C,B,F,A,D,E
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document.write( "C B F A D E\r\n" );
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document.write( "There is just 1 way that can happen.\r\n" );
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document.write( "The probability of that is 1 way out of 720 or 1/720.\r\n" );
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\n" ); document.write( "D.Comic D or E will perform fourth.
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document.write( "_ _ _ D _ _  \r\n" );
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document.write( "There are 5! = 120 ways to fill those 5 blanks with the letters A,B,C,E,F.\r\n" );
document.write( "In addition to those, there are another 5! = 120 ways to fill these 5 blanks\r\n" );
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document.write( "_ _ _ E _ _ \r\n" );
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document.write( "with the letters A,B,C,D,F.\r\n" );
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document.write( "That's 2(5!) = 2(120) = 240 ways.\r\n" );
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document.write( "The probability of one of those is 240 ways out of 720 or 240/720 or 1/3.\r\n" );
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document.write( "Edwin
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