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how many 5-digit numbers of 1,2,3,4,5,6 and 7 the number must contain a 6 and
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document.write( "I am assuming that we cannot repeat a digit.\r\n" );
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document.write( "First we'll find the number of 4 digit numbers that do not contain a \r\n" );
document.write( "5 or a 6 and then\r\n" );
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document.write( "multiply by the number of ways we can insert a 6 in each, which is 5 ways:\r\n" );
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document.write( "For example in the 4 digit number 2371 can have a 6 inserted in 5 ways:\r\n" );
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document.write( "62371, 26371, 23671, 23761, 23716\r\n" );
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document.write( "The number pf 4-digit numbers we can make from {1,2,3,4,7} is\r\n" );
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document.write( "5 ways to choose the 1st digit.\r\n" );
document.write( "4 ways to choose the 2nd digit.\r\n" );
document.write( "3 ways to choose the 3rd digit.\r\n" );
document.write( "2 ways to choose the 4th digit.\r\n" );
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document.write( "5P4 = 5*4*3*2 = 120 ways.\r\n" );
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document.write( "Then we can insert a 6 to make a 5-digit number 5 ways:\r\n" );
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document.write( "Answer 6*360 = 2160 ways.\r\n" );
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document.write( "\n" ); document.write( "how many 5-digit numbers of 1,2,3,4,5,6 and 7. The digit 3 must be in the
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\n" ); document.write( "and not a 5. no digit can repeat:
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document.write( "-34--\r\n" );
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document.write( "We can choose the place to put the 6 in 3 ways.\r\n" );
document.write( "That leaves 2 blanks to fill, a leftmost blank and a rightmost blank.\r\n" );
document.write( "We can choose the digit to put in the leftmost remaining blank in 3 \r\n" );
document.write( "remaining ways: {1,2,7}\r\n" );
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document.write( "We can choose the digit to put in the rightmost remaining blank in 2\r\n" );
document.write( "ways.\r\n" );
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document.write( "That's 3*3*2 = 18 ways. \r\n" );
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document.write( "Edwin \n" );
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