document.write( "Question 1014286: How many 3-digit numbers can be formed from the digits
\n" ); document.write( "0,1,2,3,4,5,6 if each digit can be used only once?\r
\n" ); document.write( "\n" ); document.write( "(ii) How many of these are odd numbers ? \r
\n" ); document.write( "\n" ); document.write( "(iii) How many are greater than 330 ? \n" ); document.write( "
Algebra.Com's Answer #634158 by Edwin McCravy(20055)\"\" \"About 
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\n" ); document.write( "How many 3-digit numbers can be formed from the digits
\n" ); document.write( "0,1,2,3,4,5,6 if each digit can be used only once?
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document.write( "There are 7 unchosen digits\r\n" );
document.write( "Choose the first digit any of 6 ways other than 0. \r\n" );
document.write( "That leaves 6 unchosen digits\r\n" );
document.write( "Choose the second digit any of 6 ways. Can choose 0.\r\n" );
document.write( "That leaves 5 unchosen digits.\r\n" );
document.write( "Choose the third digit any of 5 ways.\r\n" );
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document.write( "Answer: (6)(6)(5) = 180 ways\r\n" );
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\n" ); document.write( "(ii) How many of these are odd numbers ?
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document.write( "There are 7 unchosen digits.\r\n" );
document.write( "Choose the last digit any of 3 ways, 1,3,or 5\r\n" );
document.write( "That leaves 6 unchosen digits, including 0.\r\n" );
document.write( "Choose the first digit any of 5 ways. (Can't choose 0).\r\n" );
document.write( "That leaves 5 unchosen digits including 0.\r\n" );
document.write( "Choose the middle digit any of these 5 unchosen ways.\r\n" );
document.write( "Answer: (3)(5)(5) = 75 ways\r\n" );
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\n" ); document.write( "(iii) How many are greater than 330 ?
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document.write( "Case 1:  All those between 330 and 400\r\n" );
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document.write( "Choose the first digit 1 way (as 3)\r\n" );
document.write( "That leaves 6 unchosen digits.\r\n" );
document.write( "Choose the second digit any of 3 ways, 4,5, or 6\r\n" );
document.write( "That leaves 5 unchosen digits\r\n" );
document.write( "Choose the third digit any of these 5 ways.\r\n" );
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document.write( "Answer case 1: (1)(3)(5) = 15 ways.\r\n" );
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document.write( "Case 2: Those greater than 400\r\n" );
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document.write( "Choose the first digit any of 3 ways, 4,5, or 6\r\n" );
document.write( "That leaves 6 remaining unchosen digits.\r\n" );
document.write( "Choose the second digit any of these 6 remaining unchosen digits.\r\n" );
document.write( "That leaves 5 remaining unchosen digits.\r\n" );
document.write( "Choose the third digit any of these 5 remaining unchosen digits.\r\n" );
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document.write( "Answer to case 2:  (3)(6)(5) = 90 ways.\r\n" );
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document.write( "Total for part (iii):  15+90 = 105 ways. \r\n" );
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document.write( "Edwin
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