document.write( "Question 206863: How many ways can the numbers 1, 2, 3, 4 and 5 be placed in a line so that neither 1 nor 5 occupy either the first or the last place in the sequence?\r
\n" ); document.write( "\n" ); document.write( "(A) 6 (B) 24 (C) 36 (D) 54 (E) 72 \n" ); document.write( "

Algebra.Com's Answer #156389 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
How many ways can the numbers 1, 2, 3, 4 and 5 be placed in a line so that neither 1 nor 5 occupy either the first or the last place in the sequence?
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document.write( "We can choose the 1st number 3 ways.  That's 3.\r\n" );
document.write( "We can choose the 5th number 2 ways.  That's 3*2.\r\n" );
document.write( "We can choose the 2nd number 3 ways (we've used two already).  That's 3*2*3\r\n" );
document.write( "We can choose the 3rd number 2 ways.  That's 3*2*3*2\r\n" );
document.write( "We can choose the 4th number 1 way.  That's 3*2*3*2*1\r\n" );
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document.write( "Multiply that out and get 36. That's 36 ways.  Here they all are:\r\n" );
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document.write( " 1.  2, 1, 3, 5, 4\r\n" );
document.write( " 2.  2, 1, 4, 5, 3\r\n" );
document.write( " 3.  2, 1, 5, 3, 4\r\n" );
document.write( " 4.  2, 1, 5, 4, 3\r\n" );
document.write( " 5.  2, 3, 1, 5, 4\r\n" );
document.write( " 6.  2, 3, 5, 1, 4\r\n" );
document.write( " 7.  2, 4, 1, 5, 3 \r\n" );
document.write( " 8.  2, 4, 5, 1, 3\r\n" );
document.write( " 9.  2, 5, 1, 3, 4\r\n" );
document.write( "10.  2, 5, 1, 4, 3\r\n" );
document.write( "11.  2, 5, 3, 1, 4\r\n" );
document.write( "12.  2, 5, 4, 1, 3\r\n" );
document.write( "13.  3, 1, 2, 5, 4\r\n" );
document.write( "14.  3, 1, 4, 5, 2\r\n" );
document.write( "15.  3, 1, 5, 2, 4\r\n" );
document.write( "16.  3, 1, 5, 4, 2\r\n" );
document.write( "17.  3, 2, 1, 5, 4\r\n" );
document.write( "18.  3, 2, 5, 1, 4\r\n" );
document.write( "19.  3, 4, 1, 5, 2\r\n" );
document.write( "20.  3, 4, 5, 1, 2\r\n" );
document.write( "21.  3, 5, 1, 2, 4\r\n" );
document.write( "22.  3, 5, 1, 4, 2\r\n" );
document.write( "23.  3, 5, 2, 1, 4\r\n" );
document.write( "24.  3, 5, 4, 1, 2\r\n" );
document.write( "25.  4, 1, 2, 5, 3\r\n" );
document.write( "26.  4, 1, 3, 5, 2\r\n" );
document.write( "27.  4, 1, 5, 2, 3\r\n" );
document.write( "28.  4, 1, 5, 3, 2\r\n" );
document.write( "29.  4, 2, 1, 5, 3\r\n" );
document.write( "30.  4, 2, 5, 1, 3\r\n" );
document.write( "31.  4, 3, 1, 5, 2\r\n" );
document.write( "32.  4, 3, 5, 1, 2\r\n" );
document.write( "33.  4, 5, 1, 2, 3\r\n" );
document.write( "34.  4, 5, 1, 3, 2\r\n" );
document.write( "35.  4, 5, 2, 1, 3\r\n" );
document.write( "36.  4, 5, 3, 1, 2\r\n" );
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document.write( "Edwin

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