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how many 7-digit telephone numbers are possible if the first digit cannot be zero and \r
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document.write( "Case 1: 1st, 3rd, 5th, 7th digits are odd \r\n" );
document.write( "Choose the 1st digit 5 ways (1,3,5,7,9}\r\n" );
document.write( "Choose the 2nd digit 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "Choose the 3rd digit 5 ways {1,3,5,7,9}\r\n" );
document.write( "Choose the 4th digit 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "Choose the 5th digit 5 ways {1,3,5,7,9}\r\n" );
document.write( "Choose the 6th digit 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "Choose the 7th digit 5 ways {1,3,5,7,9}\r\n" );
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document.write( "That's 5·10·5·10·5·10·5 = (5^4)(10^3) = 625000 for case 1\r\n" );
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document.write( "Case 2: 2nd, 4th, 6th digits are odd \r\n" );
document.write( "Choose the 1st digit 9 ways (1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "Choose the 2nd digit 5 ways {1,3,5,7,9}\r\n" );
document.write( "Choose the 3rd digit 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "Choose the 4th digit 5 ways {1,3,5,7,9}\r\n" );
document.write( "Choose the 5th digit 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "Choose the 6th digit 5 ways {1,3,5,7,9}\r\n" );
document.write( "Choose the 7th digit 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
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document.write( "That's 9·5·10·5·10·5·10 = 9(5^3)(10^3) = 1125000 for case 2\r\n" );
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document.write( "Total = 625000 + 1125000 = 1750000 \r\n" );
document.write( "\n" ); document.write( "B)the telephone number must start with 226 and end with 5
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document.write( "226---5\r\n" );
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document.write( "We only need to choose the 4th, 5th and 6th digits.\r\n" );
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document.write( "Choose the 4th digit 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "Choose the 5th digit 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "Choose the 6th digit 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
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document.write( "Answer: 10·10·10 = 10^3 = 1000\r\n" );
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document.write( "C) no repetitions are allowed\r\n" );
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document.write( "Choose the 1st digit as any of the 9 unused digits.\r\n" );
document.write( " (1,2,3,4,5,6,7,8,9} (can't be 0)\r\n" );
document.write( "Choose the 2nd digit as any of the 9 unused digits. (can be 0)\r\n" );
document.write( "Choose the 3rd digit as any of the 8 unused digits. \r\n" );
document.write( "Choose the 4th digit as any of the 7 unused digits. \r\n" );
document.write( "Choose the 5th digit as any of the 6 unused digits. \r\n" );
document.write( "Choose the 6th digit as any of the 5 unused digits. \r\n" );
document.write( "Choose the 7th digit as any of the 4 unused digits.\r\n" );
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document.write( "Answer 9·9·8·7·6·5·4 = 544320\r\n" );
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document.write( "Edwin \n" );
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