document.write( "Question 890985: A binary number consists only 0s and 1s.
\n" ); document.write( "A) How may different seven-digit binary numbers are there?
\n" ); document.write( "B) How may different seven-digit binary numbers are there which begin with a 1 and which contain exactly four 1s.
\n" ); document.write( "C) How may different seven-digit binary numbers are there which contain exactly four 1s which are all adjacent(next to each other)? \n" ); document.write( "
Algebra.Com's Answer #539449 by Edwin McCravy(20055)\"\" \"About 
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A binary number consists only 0s and 1s.
\n" ); document.write( "A) How may different seven-digit binary numbers are there?
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document.write( "The first digit cannot be 0, and must be 1.\r\n" );
document.write( "There is 1 way to choose the first digit.\r\n" );
document.write( "There are 2 ways to choose the second digit, either 0 or 1.\r\n" );
document.write( "There are 2 ways to choose the third digit, either 0 or 1.\r\n" );
document.write( "There are 2 ways to choose the fourth digit, either 0 or 1.\r\n" );
document.write( "There are 2 ways to choose the fifth digit, either 0 or 1.\r\n" );
document.write( "There are 2 ways to choose the sixth digit, either 0 or 1.\r\n" );
document.write( "There are 2 ways to choose the seventh digit, either 0 or 1.\r\n" );
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document.write( "That's 1󫎾󫎾󫎾 = 26 = 64 seven-digit numbers.\r\n" );
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\n" ); document.write( "B) How may different seven-digit binary numbers are there which begin with a 1
\n" ); document.write( "and which contain exactly four 1s.
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document.write( "1 _ _ _ _ _ _\r\n" );
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document.write( "There are 6 positions to place the other 3 1's.\r\n" );
document.write( "That's 6 positions choose 3 or C(6,3) = 20.  We\r\n" );
document.write( "place 0's in the remaining 3 positions.\r\n" );
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document.write( "Answer: 20\r\n" );
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\n" ); document.write( "C) How may different seven-digit binary numbers are there which contain exactly
\n" ); document.write( "four 1s which are all adjacent(next to each other)?
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document.write( "The first digit must be 1, and since all four 1's must be together, \r\n" );
document.write( "there is only 1,\r\n" );
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document.write( "1111000\r\n" );
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document.write( "Answer: 1\r\n" );
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document.write( "Edwin
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