document.write( "Question 1100062: Three bands and two comics are performing for a student
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Algebra.Com's Answer #714593 by Edwin McCravy(20062) $\"\"$ $\"About$

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Three bands and two comics are performing for a student
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5 acts, permute all 5.  That's 5P5 = 5! = 120 ways.\r\n" );
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How many if the comics must perform between bands?

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document.write( "Choose the band to perform first in 3 ways.\r\n" );
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document.write( "For each of those 3 choices for the 1st act, there are \r\n" );
document.write( "2 ways to choose the comic for the 2nd. \r\n" );
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document.write( "So that's 3×2 or 6 ways to choose the first 2 acts.\r\n" );
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document.write( "For each of those 3×2 or 6 ways to choose the band to go\r\n" );
document.write( "first and the comic to go second, there remain 2 bands to\r\n" );
document.write( "choose to go 3rd.  \r\n" );
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document.write( "So that's 3×2×2 or 6×3 or 18 ways to choose the first 3\r\n" );
document.write( "acts.\r\n" );
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document.write( "For each of those 3×2×2 or 12 ways to choose the 1st 3\r\n" );
document.write( "acts, there remains only 1 comic to choose to go 4th.  \r\n" );
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document.write( "So that's 3×2×2×1 or 18×1 or 18 ways to choose the first 4\r\n" );
document.write( "acts.\r\n" );
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document.write( "Finally there is only 1 way to choose the last act, which \r\n" );
document.write( "is the only remaining band.\r\n" );
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document.write( "Answer:  3×2×2×1×1 or 12 ways.\r\n" );
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document.write( "Checking by writing them out:\r\n" );
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document.write( " 1.  Band A, Comic 1, Band B, Comic 2, Band C.\r\n" );
document.write( " 2.  Band A, Comic 2, Band B, Comic 1, Band C.\r\n" );
document.write( " 3.  Band A, Comic 1, Band C, Comic 2, Band B.\r\n" );
document.write( " 4.  Band A, Comic 2, Band C, Comic 1, Band B.\r\n" );
document.write( " 5.  Band B, Comic 1, Band A, Comic 2, Band C.\r\n" );
document.write( " 6.  Band B, Comic 2, Band A, Comic 1, Band C.\r\n" );
document.write( " 7.  Band B, Comic 1, Band C, Comic 2, Band A.\r\n" );
document.write( " 8.  Band B, Comic 2, Band C, Comic 1, Band A.\r\n" );
document.write( " 9.  Band C, Comic 1, Band A, Comic 2, Band B.\r\n" );
document.write( "10.  Band C, Comic 2, Band A, Comic 1, Band B.\r\n" );
document.write( "11.  Band C, Comic 1, Band B, Comic 2, Band A.\r\n" );
document.write( "12.  Band C, Comic 2, Band B, Comic 1, Band A. \r\n" );
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document.write( "Edwin

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