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You can put this solution on YOUR website!
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document.write( "Since order matters, we should not use the word \"combination\", In\r\n" );
document.write( "algebra, the word \"combination\" is used only when the order does \r\n" );
document.write( "not matter.\r\n" );
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document.write( "But the order does matter here, so we should use the word \"permutation\"\r\n" );
document.write( "instead of \"combination\"\r\n" );
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document.write( "Case 1: None of the digits are the same:\r\n" );
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document.write( "These are the arrangements of {0,2,4}\r\n" );
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document.write( "Choose the first digit 3 ways\r\n" );
document.write( "Choose the second digit 2 ways\r\n" );
document.write( "Choose the third digit 1 way.\r\n" );
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document.write( "3×2×1 = 6 ways for case 1. Those 6 are\r\n" );
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document.write( "024, 042, 204, 240, 402, 420\r\n" );
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document.write( "Case 2: Exactly two 0's\r\n" );
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document.write( "Choose the remaining digit 2 ways. {2,4}\r\n" );
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document.write( "We can arrange them in 3!/2! = 3 ways\r\n" );
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document.write( "That's 2×3 = 6 for case 2. Those 6 are:\r\n" );
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document.write( "002, 004, 020, 040, 200, 400\r\n" );
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document.write( "Case 3. Exactly 2 2's:\r\n" );
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document.write( "Choose the remaining digit 2 ways. {0,4}\r\n" );
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document.write( "We can arrange them in 3!/2! = 3 ways\r\n" );
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document.write( "That's 2×3 = 6 for case 3. Those 6 are:\r\n" );
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document.write( "022, 224, 202, 242, 220, 422\r\n" );
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document.write( "Case 4. All 3 2's:\r\n" );
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document.write( "That's just 1 way, 222.\r\n" );
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document.write( "Grand total = 6+6+6+1 = 19 ways.\r\n" );
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document.write( "Edwin \n" );
document.write( "