document.write( "Question 459560: How many 4-digit whole numbers using the digits in the set {1,2,3,4,5,6,7,8,9,0}can be formed using the restrictions below.
\n" ); document.write( "For purposes of this problem, the whole number can be \"padded\" with zeros on the left. So a 0014 is a good number,(IE numbers can start with zeros).
\n" ); document.write( "Each part below is is independant of the previous part.\r
\n" ); document.write( "\n" ); document.write( "a. Numbers do not contain the same digit twice, (without replacement)\r
\n" ); document.write( "\n" ); document.write( "b. Numbers end with an even digit and can repeat digits, (with replacement)\r
\n" ); document.write( "\n" ); document.write( "c. Numbers begin with an odd digit and can repeat digits, (with replacement)\r
\n" ); document.write( "\n" ); document.write( "d. Numbers begin and end with a 1, (with replacement)\r
\n" ); document.write( "\n" ); document.write( "e. Numbers have exactly three digits which are 7s (with replacement) \n" ); document.write( "
Algebra.Com's Answer #315135 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
How many 4-digit whole numbers using the digits in the set {1,2,3,4,5,6,7,8,9,0}can be formed using the restrictions below.
\n" ); document.write( "For purposes of this problem, the whole number can be \"padded\" with zeros on the left. So a 0014 is a good number,(IE numbers can start with zeros).
\n" ); document.write( "Each part below is is independant of the previous part.
\n" ); document.write( "
\n" ); document.write( "a. Numbers do not contain the same digit twice, (without replacement)
\n" ); document.write( "
\r\n" );
document.write( "Examples would be 0692, 8591\r\n" );
document.write( "\r\n" );
document.write( "Choose digit #1 10 ways, and then choose digit #2 9 ways, \r\n" );
document.write( "and then choose digit #3 8 ways, and then choose digit #4\r\n" );
document.write( "7 ways.There are 10×9×8×7 = 5040 ways. \r\n" );
document.write( "

\n" ); document.write( "b. Numbers end with an even digit and can repeat digits, (with replacement)
\n" ); document.write( "
\r\n" );
document.write( "Examples would be 8736, 4994, 7770, 0000, 2010\r\n" );
document.write( "\r\n" );
document.write( "We do not have to choose the digits in any certain order. \r\n" );
document.write( "So we will choose digit #4, then digit #1, then digit #2,\r\n" );
document.write( "and finally digit #3.\r\n" );
document.write( "\r\n" );
document.write( "Choose digit #4 5 ways (2,4,6,8, or 0), and then choose \r\n" );
document.write( "digit #1 10 ways, and then choose digit #2 10 ways, and \r\n" );
document.write( "then choose digit #3 10 ways. There are \r\n" );
document.write( "5×10×10×10 = 5000 ways.\r\n" );
document.write( "

\n" ); document.write( "c. Numbers begin with an odd digit and can repeat digits,
\n" ); document.write( "(with replacement)
\n" ); document.write( "
\r\n" );
document.write( "Examples:  1887, 9742, 5555\r\n" );
document.write( "\r\n" );
document.write( "Choose digit #1 5 ways (1,3,5,7,9), and then choose \r\n" );
document.write( "digit #2 10 ways, and then choose digit #3 10 ways, and \r\n" );
document.write( "then choose digit #4 10 ways.  There are \r\n" );
document.write( "5×10×10×10 = 5000 ways.\r\n" );
document.write( "

\n" ); document.write( "d. Numbers begin and end with a 1, (with replacement)
\n" ); document.write( "
\r\n" );
document.write( "Examples:  1871, 1661, 1111\r\n" );
document.write( "\r\n" );
document.write( "Choose digit #1 1 way, and then choose digit #2 10 ways, \r\n" );
document.write( "and then choose digit #3 10 ways, and then choose digit \r\n" );
document.write( "#4 1 way. There are 1×10×10×1 = 100 ways.\r\n" );
document.write( "

\n" ); document.write( "e. Numbers have exactly three digits which are 7s (with replacement)
\n" ); document.write( "
\r\n" );
document.write( "Examples: 7771, 7707, 7477, 0777\r\n" );
document.write( "\r\n" );
document.write( "There are three 7's and one non-7.  We choose the position \r\n" );
document.write( "for the non-7 any of 4 ways, and then the digit for the non-7\r\n" );
document.write( "9 ways, then 1 way each for the 7's.\r\n" );
document.write( "There are 4×9×1×1 = 36 ways. \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );