document.write( "Question 1143267: a) How many three digit numbers can be formed from the digits 2,3,4,5,6,7 and 8? No digit repeats in the same number.
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Algebra.Com's Answer #764050 by Edwin McCravy(20060)\"\" \"About 
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a) How many three digit numbers can be formed from the digits 2,3,4,5,6,7 and 8? No digit repeats in the same number.
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document.write( "There are 7 digits.\r\n" );
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document.write( "Choose the 1st digit any of the 7 digits.  That's 7 ways.\r\n" );
document.write( "Having chosen 1 digit, and since no digits can be repeated,\r\n" );
document.write( "there remain only 6 digits to choose from.\r\n" );
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document.write( "Choose the 2nd digit any of the remaining 6 digits.  That's 6 ways.\r\n" );
document.write( "Having chosen 2 digits, and since no digits can be repeated,\r\n" );
document.write( "there remain only 5 digits to choose from. \r\n" );
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document.write( "Choose the 3rd digit any of the remaining 5 digits. That's 5 ways.\r\n" );
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document.write( "That's 7×6×5 = 7P3 = 210\r\n" );
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\n" ); document.write( "b) What is the probability of an even number?
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document.write( "We first answer the question: \"How many even three-digit numbers can\r\n" );
document.write( "we have.  We choose the most restrictive thing first, which is the\r\n" );
document.write( "3rd digit, for it must be even.\r\n" );
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document.write( "Choose the 3rd digit any of the 4 even digits 2,4,6,8.  That's 4 ways.\r\n" );
document.write( "Having chosen 1 digit, and since no digits can be repeated,\r\n" );
document.write( "there remain only 6 digits to choose from.\r\n" );
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document.write( "Choose the 1st digit any of the remaining 6 digits.  That's 6 ways.\r\n" );
document.write( "Having chosen 2 digits, and since no digits can be repeated,\r\n" );
document.write( "there remain only 5 digits to choose from.\r\n" );
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document.write( "Choose the 2nd digit any of the remaining 5 digits.  That's 5 ways.\r\n" );
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document.write( "So that's 4×6×5 = 120 ways\r\n" );
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document.write( "So the probability of an even number is 120 out of 720 or\r\n" );
document.write( "120/720 which reduces to 1/6.\r\n" );
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\n" ); document.write( "c) What is the probability of numbers greater than 550 but less than 770?
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document.write( "The first digit is either 5, 6 or 7, but we must take each of those\r\n" );
document.write( "as a separate case because with each, the number of choices for the\r\n" );
document.write( "2nd digit changes.\r\n" );
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document.write( "Case 1.  the first digit is 5.\r\n" );
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document.write( "Choose the first digit as 5. That's 1 way.\r\n" );
document.write( "Choose the 2nd digit any of the 3 digits 6,7,8.  That's 3 ways.\r\n" );
document.write( "Having chosen 2 digits, and since no digits can be repeated,\r\n" );
document.write( "there remain only 5 digits to choose from for the 3rd digit.\r\n" );
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document.write( "That's 1×3×5 = 15 ways for case 1.\r\n" );
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document.write( "Case 2.  the first digit is 6.\r\n" );
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document.write( "Choose the first digit as 6.  That's 1 way.\r\n" );
document.write( "Choose the 2nd digit as any of the 6 digits 2,3,4,5,7,8.  That's 6 ways.\r\n" );
document.write( "Having chosen 2 digits, and since no digits can be repeated,\r\n" );
document.write( "there remain only 5 digits to choose from for the 3rd digit.\r\n" );
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document.write( "That's 1×6×5 = 30 ways for case 2. \r\n" );
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document.write( "Case 3.  the first digit is 7.\r\n" );
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document.write( "Choose the first digit as 7.  That's 1 way\r\n" );
document.write( "Choose the 2nd digit any of the 5 digits 2,3,4,5,6.  That's 5 ways.\r\n" );
document.write( "Having chosen 2 digits, and since no digits can be repeated,\r\n" );
document.write( "there remain only 5 digits to choose from. That's 5 ways.\r\n" );
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document.write( "That's 1×5×5 = 25 ways for case 3.\r\n" );
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document.write( "So for all three cases, that's a grand total of 15+30+25 = 70 ways\r\n" );
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document.write( "So the probability of a number bettween 550 and 770 is \r\n" );
document.write( "70 ways out of 210 or 70/210 which reduces to 1/3.\r\n" );
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document.write( "Edwin

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