document.write( "Question 1027795: In how many 5-digit numbers can be formed from the 10 digits (0-9), if
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\n" ); document.write( "ii) How many different sets of 4 students can be chosen out of 17 qualified students to represent a school in a mathematics contest
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Algebra.Com's Answer #643013 by Edwin McCravy(20056)\"\" \"About 
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In how many 5-digit numbers can be formed from the 10 digits (0-9), if
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document.write( "Two ways to get it:\r\n" );
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document.write( "First way:\r\n" );
document.write( "The smallest is 10000 and the largest is 99999\r\n" );
document.write( "There are 99999 integers from 1 to 99999 inclusive.\r\n" );
document.write( "The integers from 1 to 9999 inclusive have fewer than 5 digits.\r\n" );
document.write( "There are 9999 integers that have fewer than 5 digits.\r\n" );
document.write( "99999-9999 = 90000 = the number of 5 digit integers.\r\n" );
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document.write( "Second way:\r\n" );
document.write( "We can choose the 1st digit any of 9 ways, 1-9.\r\n" );
document.write( "We can choose the 2nd digit any of 10 ways, 0-9.\r\n" );
document.write( "We can choose the 3rd digit any of 10 ways, 0-9.\r\n" );
document.write( "We can choose the 4th digit any of 10 ways, 0-9.\r\n" );
document.write( "We can choose the 5th digit any of 10 ways, 0-9.\r\n" );
document.write( "Answer 9*10*10*10*10 = 90000\r\n" );
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\n" ); document.write( "b) The numbers begin with 40;
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document.write( "Two ways to get it:\r\n" );
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document.write( "First way:\r\n" );
document.write( "The smallest is 40000 and the largest is 40999\r\n" );
document.write( "There are 40999 integers from 1 to 40999 inclusive.\r\n" );
document.write( "The integers from 1 to 39999 inclusive are less than 40000.\r\n" );
document.write( "There are 39999 integers that are less than 40000.\r\n" );
document.write( "40999-39999 = 10000 = the number that begin with 40.\r\n" );
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document.write( "Second way:\r\n" );
document.write( "We can choose the 1st digit only 1 way, as 4.\r\n" );
document.write( "We can choose the 2nd digit only 1 way, as 0.\r\n" );
document.write( "We can choose the 3rd digit any of 10 ways, 0-9.\r\n" );
document.write( "We can choose the 4th digit any of 10 ways, 0-9.\r\n" );
document.write( "We can choose the 5th digit any of 10 ways, 0-9.\r\n" );
document.write( "Answer 1*1*10*10*10 = 10000\r\n" );
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\n" ); document.write( "c) The numbers are even;
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document.write( "Two ways to get it:\r\n" );
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document.write( "First way:\r\n" );
document.write( "Half of the 90000 in the first part are even and half are odd.\r\n" );
document.write( "Half of 90000 is 45000\r\n" );
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document.write( "Second way:\r\n" );
document.write( "All even integers end in either 0,2,4,6 or 8.\r\n" );
document.write( "We can choose the 1st digit any of 9 ways, 1-9.\r\n" );
document.write( "We can choose the 2nd digit any of 10 ways, 0-9.\r\n" );
document.write( "We can choose the 3rd digit any of 10 ways, 0-9.\r\n" );
document.write( "We can choose the 4th digit any of 10 ways, 0-9.\r\n" );
document.write( "We can choose the 5th digit any of 5 ways, 0,2,4,6, or 8.\r\n" );
document.write( "Answer 9*10*10*10*5 = 45000\r\n" );
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\n" ); document.write( "d) The numbers are divisible by 5.
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document.write( "Two ways to get it:\r\n" );
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document.write( "First way:\r\n" );
document.write( "Every 5th integer is divisible by 5.  Therefore:\r\n" );
document.write( "One-fifth of the 90000 in the first part are divisible by 5.\r\n" );
document.write( "One-fifth of 90000 is 18000\r\n" );
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document.write( "Second way.\r\n" );
document.write( "All integers divisible by 5 end in either 0 or 5.\r\n" );
document.write( "We can choose the 1st digit any of 9 ways, 1-9.\r\n" );
document.write( "We can choose the 2nd digit any of 10 ways, 0-9.\r\n" );
document.write( "We can choose the 3rd digit any of 10 ways, 0-9.\r\n" );
document.write( "We can choose the 4th digit any of 10 ways, 0-9.\r\n" );
document.write( "We can choose the 5th digit any of 2 ways, 0 or 5.\r\n" );
document.write( "Answer 9*10*10*10*2 = 18000 \r\n" );
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\n" ); document.write( "ii) How many different sets of 4 students can be chosen out
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document.write( "17 students choose 4 = 17C4 = 1001.\r\n" );
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document.write( "Edwin
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