document.write( "Question 1042231: You bought six numbers at your local hardware store. The numbers are 0, 1, 2, 3, 4, 5.
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\n" ); document.write( "b) Using the same digits as above, how many 4 digit numbers smaller than 3500 could
\n" ); document.write( "you form if repetition was not allowed? (note: 0351 is not considered a house number).
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Algebra.Com's Answer #657217 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
You bought six numbers at your local hardware store.
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\n" ); document.write( "a) How many 6 digit house numbers would be even?
\n" ); document.write( " (note: 0351 is not considered a house number as you
\n" ); document.write( "only use each number once).
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document.write( "First we find the number of ways to choose the 1st\r\n" );
document.write( "and 6th (last) digits.\r\n" );
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document.write( "Case 1.  We choose 2 or 4 for the first digit\r\n" );
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document.write( "We choose the first digit 2 ways, 2 or 4\r\n" );
document.write( "We choose the last digit 2 ways, 0 and whichever \r\n" );
document.write( "of 2,4 we did not choose for the first digit.\r\n" );
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document.write( "That's 2*2 = 4 ways for case 1.\r\n" );
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document.write( "Case 2. We choose 1,3, or 5 for the 1st digit\r\n" );
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document.write( "We choose the 1st digit 3 ways, 1,3 or 5\r\n" );
document.write( "We choose the 6th (last) digit 3 ways, 0, 2, or 4 \r\n" );
document.write( "   choose for the first digit.\r\n" );
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document.write( "That's 3*3 = 9 ways for case 2.\r\n" );
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document.write( "Total number of ways to choose 1st and 6th (last) digits =\r\n" );
document.write( "4+9 = 13 ways to choose 1st and 6th (last) digits.\r\n" );
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document.write( "For each of those 13 ways to choose the 1st and 6th digits,\r\n" );
document.write( "we can choose the 2nd digit any of the 4 remaining ways.\r\n" );
document.write( "we can choose the 3rd digit any of the 3 remaining ways.\r\n" );
document.write( "we can choose the 4th digit either of the 2 remaining ways.\r\n" );
document.write( "we can choose the 5th digit only 1 remaining way.\r\n" );
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document.write( "Answer:  13*4*3*2*1 = 312 ways.\r\n" );
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\n" ); document.write( "b) Using the same digits as above, how many 4 digit
\n" ); document.write( "numbers smaller than 3500 could you form if repetition
\n" ); document.write( "was not allowed? (note: 0351 is not considered a house
\n" ); document.write( "number).
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document.write( "This does not say anything about the number being even or odd,\r\n" );
document.write( "so we will assume it can be either even or odd.\r\n" );
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document.write( "First we find the number of ways to choose the 1st\r\n" );
document.write( "and 2nd digits.\r\n" );
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document.write( "Case 1. The first digit is 3\r\n" );
document.write( "        We choose the first digit as 3.  That's 1 way.\r\n" );
document.write( "        We choose the 2nd digit as 0, 1, 2, or 4.  That's 4 ways.\r\n" );
document.write( "That's 1*4 = 4 ways for case 1.\r\n" );
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document.write( "Case 2. The first digit is 1 or 2\r\n" );
document.write( "        We choose the first digit as 1 or 2.  That's 2 ways\r\n" );
document.write( "        We choose the 2nd digit as any of the 5 remaining digits.\r\n" );
document.write( "That's 2*5 = 10 ways for case 2.\r\n" );
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document.write( "Total for cases 1 and 2 = 4+10 = 14\r\n" );
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document.write( "For each of those 14 ways to choose the 1st and 2nd digits,\r\n" );
document.write( "we can choose the 3rd digit any of the 4 remaining ways.\r\n" );
document.write( "we can choose the 4th digit any of the 3 remaining ways.\r\n" );
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document.write( "Answer: 14*4*3 = 168 ways\r\n" );
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document.write( "Edwin
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