document.write( "Question 855773: In the word DISCRETE how many :\r
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Algebra.Com's Answer #516811 by Edwin McCravy(20055) $\"\"$ $\"About$

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In the word DISCRETE how many :\r
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\n" ); document.write( "3. 6 letter word can be formed
\n" ); document.write( "4. 5 letter word can be formed
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document.write( "The 2 E's are indistinguishable.  So anytime we use both E's we\r\n" );
document.write( "must divide by 2!.\r\n" );
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document.write( "1. The number of 8 letter words is  = 20160\r\n" );
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document.write( "2. The number of 7 letter words must be broken down into two\r\n" );
document.write( "   cases:\r\n" );
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document.write( "   Case 1: Only one E is used: 7! = 5040\r\n" );
document.write( "   Case 2: Both E's are used.\r\n" );
document.write( "           We can choose the 5 other letters to use from these\r\n" );
document.write( "           six {D,I,S,C,R,T}.  That's C(6,5) = 6 ways.\r\n" );
document.write( "           For each of those 6 ways there are  = 2520\r\n" );
document.write( "           ways to arrange them.\r\n" );
document.write( "           So for case 2 we have 6×2520 = 15120\r\n" );
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document.write( "Total = 5040 + 15120 = 20160\r\n" );
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document.write( "3. The number of 6 letter words must also be broken down into two\r\n" );
document.write( "   cases:\r\n" );
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document.write( "   Case 1: No more than 1 E is used.\r\n" );
document.write( "           We choose the 6 letters to use from these {D,I,S,C,R,E,T}\r\n" );
document.write( "           That's C(7,6) = 7 ways\r\n" );
document.write( "           For each of those 7 ways there are 6! = 720 ways\r\n" );
document.write( "           to arrange them.\r\n" );
document.write( "           So for case 1, there are 7×720 = 5040 ways.\r\n" );
document.write( "   Case 2: Both E's are used.\r\n" );
document.write( "           We can choose the 4 other letters to use from these\r\n" );
document.write( "           six {D,I,S,C,R,T}.  That's C(6,4) = 6 ways.\r\n" );
document.write( "           For each of those 6 ways there are  = 360\r\n" );
document.write( "           ways to arrange them.\r\n" );
document.write( "           So for case 2 we have 6×360 = 2160 ways.\r\n" );
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document.write( "Total = 5040+2160 = 7200 ways.\r\n" );
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document.write( "I'll let you do the 5-letter words.\r\n" );
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document.write( "Edwin

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