document.write( "Question 1062364: i have a sets of number 1,2,7,7,7. what is the formula to count how many 3-digit number possible combinations using that sets, with these conditions of combinations must be unique. the result (13 combinations) are
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\n" ); document.write( "172
\n" ); document.write( "177
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\n" ); document.write( "271
\n" ); document.write( "277
\n" ); document.write( "712
\n" ); document.write( "717
\n" ); document.write( "721
\n" ); document.write( "727
\n" ); document.write( "771
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\n" ); document.write( "777
\n" ); document.write( "And if i a have a set of 1,2,3,7,7,7, there will be 34 possible combinations.
\n" ); document.write( "thanks in advance. \n" ); document.write( "
Algebra.Com's Answer #677307 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
I have a sets of number 1,2,7,7,7. what is the formula to count how many
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document.write( "For the number of 3-digit numbers with exactly 1 7:\r\n" );
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document.write( "Choose the position to put the 7 in 3C1=3 ways.\r\n" );
document.write( "Choose a non-7 for the left-most remaining position in 2C1=2 ways.\r\n" );
document.write( "Choose a non-7 for the right-most remaining position in 1C1=1 ways.\r\n" );
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document.write( "(3C1)(2C1)(1C1) = (3)(2)(1) = 6 ways.\r\n" );
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document.write( "For the number of 3-digit numbers with exactly 2 7's:\r\n" );
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document.write( "Choose the positions to put the 7's in 3C2=3 ways.\r\n" );
document.write( "Choose a non-7 for the only remaining position in 2C1=2 ways.\r\n" );
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document.write( "(3C2)(2C1) = (3)(2) = 6 ways.\r\n" );
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document.write( "For the number of 3-digit numbers with exactly 3 7's:\r\n" );
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document.write( "3C3 = 1 way.  That's 777.\r\n" );
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document.write( "Answer: 6+6+1 = 13 ways.\r\n" );
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\n" ); document.write( "And if I have a set of 1,2,3,7,7,7, there will be 34 possible combinations.
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document.write( "For the number of 3-digit numbers with exactly 0 (no) 7s:\r\n" );
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document.write( "Choose the position to put the 1 in 3C1 = 3 ways.\r\n" );
document.write( "Choose the position to put the 2 in 2C1 = 2 ways.\r\n" );
document.write( "Choose the position to put the 3 in 1C1 = 1 way.\r\n" );
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document.write( "That's (3C1)(2C1)(1C1) = (3)(2)(1) = 6\r\n" );
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document.write( "For the number of 3-digit numbers with exactly 1 7:\r\n" );
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document.write( "Choose the position to put the 7 in 3C1=3 ways.\r\n" );
document.write( "Choose a non-7 for the left-most remaining position in 3C1=3 ways.\r\n" );
document.write( "Choose a non-7 for the right-most remaining position in 2C1=2 ways.\r\n" );
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document.write( "That's (3C1)(3C1)(2C1) = (3)(3)(2) = 18 ways.\r\n" );
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document.write( "For the number of 3-digit numbers with exactly 2 7's:\r\n" );
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document.write( "Choose the positions to put the 7's in 3C2=3 ways.\r\n" );
document.write( "Choose a non-7 for the only remaining position in 3C1=3 ways.\r\n" );
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document.write( "(3C2)(3C1) = (3)(3) = 9 ways.\r\n" );
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document.write( "For the number of 3-digit numbers with exactly 3 7's:\r\n" );
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document.write( "3C3 = 1 way.  That's 777.\r\n" );
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document.write( "Answer: 6+18+9+1 = 34 ways.\r\n" );
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document.write( "Here they all are:\r\n" );
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document.write( "123, 127, 132, 137, 172, 173, 177, 213, 217, 231, \r\n" );
document.write( "237, 271, 273, 277, 312, 317, 321, 327, 371, 372, \r\n" );
document.write( "377, 712, 713, 717, 721, 723, 727, 731, 732, 737, \r\n" );
document.write( "771, 772, 773, 777.\r\n" );
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document.write( "Edwin

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