document.write( "Question 629274: Different positive four-digit integers are to be formed by using each of the digits 1,2,3,4 just once in each integer. How many different such integers can be formed if the digits 3 and 4 must NEVER be next to each other?\r
\n" ); document.write( "\n" ); document.write( "A. 4
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\n" ); document.write( "C. 12
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\n" ); document.write( "E. 24 \n" ); document.write( "
Algebra.Com's Answer #396145 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The answer would be 4! or 24 ways if it didn't matter whether 3 and 4\r\n" );
document.write( "were side by side or not.  From the 4! we must subtract the ways in which\r\n" );
document.write( " they are side by side.  There are 2 cases where they can be side by side:\r\n" );
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document.write( "Case 1. When the 3 is left of the 4, which means we are arranging these three\r\n" );
document.write( "things:  1, 2, 34 which is 3! or 6 ways.\r\n" );
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document.write( "Case 2. When the 4 is left of the 3, which means we are arranging these three\r\n" );
document.write( "things:   1, 2, 43 which is also 3! or 6 ways.\r\n" );
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document.write( "So the answer is 4! - 2×3! = 24 - 2×6 = 24 - 12 ways.\r\n" );
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document.write( "But, heck, by the time you did all that you could just have listed them all\r\n" );
document.write( "and counted them:\r\n" );
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document.write( " 1. 1324\r\n" );
document.write( " 2. 1423\r\n" );
document.write( " 3. 2314\r\n" );
document.write( " 4. 2413\r\n" );
document.write( " 5. 3124\r\n" );
document.write( " 6. 3142\r\n" );
document.write( " 7. 3214\r\n" );
document.write( " 8. 3241\r\n" );
document.write( " 9. 4123\r\n" );
document.write( "10. 4132\r\n" );
document.write( "11. 4213\r\n" );
document.write( "12. 4231\r\n" );
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document.write( "Edwin

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