document.write( "Question 890824: The following problems deal with permutations of the eight letters A, B, C, D, E, F, G and H.\r
\n" ); document.write( "\n" ); document.write( "a. What is the number of 8-permutations if A and B have to be among the first three letters? \r
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\n" ); document.write( "\n" ); document.write( "b. What is the number of 6-permutations if ‘FG’ should not be at the end? \r
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Algebra.Com's Answer #539527 by Edwin McCravy(20055) $\"\"$ $\"About$

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The following problems deal with permutations of the eight letters A, B, C, D, E, F, G and H.\r
\n" ); document.write( "\n" ); document.write( "a. What is the number of 8-permutations if A and B have to be among the first three letters?
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document.write( "Choose the position to place the A as any of the first 3 positions.\r\n" );
document.write( "Choose the position to place the B as either of the two remaining positions\r\n" );
document.write( "of the first three.\r\n" );
document.write( "Choose the position to place the C as any of the remaining 6 positions.\r\n" );
document.write( "Choose the position to place the D as any of the remaining 5 positions.\r\n" );
document.write( "Choose the position to place the E as any of the remaining 4 positions.\r\n" );
document.write( "Choose the position to place the F as any of the remaining 3 positions.\r\n" );
document.write( "Choose the position to place the G as either of the remaining 2 positions.\r\n" );
document.write( "Choose the position to place the H as the only 1 remaining position.\r\n" );
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document.write( "That's 3×2×6×5×4×3×2×1 = 6×6! = 6×720 = 4320\r\n" );
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\n" ); document.write( "b. What is the number of 6-permutations if ‘FG’ should not be at the end?
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document.write( "First we calculate the number of permutations which is 8! = 40320\r\n" );
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document.write( "Now we will calculate the number of unwanted permutations with FG at the end.\r\n" );
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document.write( "Choose the 7th position to place the F.\r\n" );
document.write( "Choose the 8th position to place the G.\r\n" );
document.write( "Choose the position to place the A as any of the first 6 positions.\r\n" );
document.write( "Choose the position to place the B as any of the 5 remaining positions\r\n" );
document.write( "of the first six.\r\n" );
document.write( "Choose the position to place the C as any of the 4 remaining positions\r\n" );
document.write( "of the first six.\r\n" );
document.write( "Choose the position to place the D as any of the 3 remaining positions\r\n" );
document.write( "of the first six.\r\n" );
document.write( "Choose the position to place the E as either of the 2 remaining positions\r\n" );
document.write( "of the first six.\r\n" );
document.write( "Choose the position to place the H as the 1 remaining positions\r\n" );
document.write( "of the first six.\r\n" );
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document.write( "That's 1×1×6×5×4×3×2×1 = 6! = 720\r\n" );
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document.write( "Now we subtract those 720 from the 40320, getting 40320-720 = 39600 \r\n" );
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\n" ); document.write( "c. What is the number of 5-permutations containing A, B and C but not adjacent to one another?
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document.write( "They must go like this:\r\n" );
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document.write( "Choose a letter for the 1st position in 3 ways  (either A,B, or C)\r\n" );
document.write( "Choose a letter for the 3rd position either of 2 ways\r\n" );
document.write( "Choose a letter for the 5th position 1 way.\r\n" );
document.write( "Choose a letter for the 2nd position any of 5 ways. (D,E,F,G, or H)\r\n" );
document.write( "Choose a letter for the 4th position any of 4 ways.  \r\n" );
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document.write( "3×2×1×5×4 = 120\r\n" );
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document.write( "Edwin

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