document.write( "Question 1175303: How many 12-bit strings (that is, bit strings of length 12) are there which:
\n" ); document.write( "have weight 7 and either start with 011 or end with 01 (or both)? \r
\n" ); document.write( "\n" ); document.write( "There were three questions before this which I have worked the answers to, but I'm confused for this part.
\n" ); document.write( "Other questions:
\n" ); document.write( "a. Q. Start with the sub-string 001? A. 2^9
\n" ); document.write( "b. Q. Have weight 7 (i.e., contain exactly 7 1's) and start with the sub-string 001? A. C(9,5)
\n" ); document.write( "c. Q. Either start with 011 or end with 01 (or both)? A. 2^9 + 2^10 - 2^7 \n" ); document.write( "

Algebra.Com's Answer #800903 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "How many 12-bit strings (that is, bit strings of length 12) are there which:
\n" ); document.write( "have weight 7 and either start with 011 or end with 01 (or both)?\r
\n" ); document.write( "\n" ); document.write( "There were three questions before this which I have worked the answers to, but I'm confused for this part.
\n" ); document.write( "Other questions:
\n" ); document.write( "a. Q. Start with the sub-string 001? A. 2^9
\n" ); document.write( "b. Q. Have weight 7 (i.e., contain exactly 7 1's) and start with the sub-string 001? A. C(9,5)
\n" ); document.write( "c. Q. Either start with 011 or end with 01 (or both)? A. 2^9 + 2^10 - 2^7
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\n" ); document.write( "\n" ); document.write( "Let me rewrite the problem (the first two lines) in a way understandable for ANYONE.\r
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document.write( "    The word of 12 symbols is written using symbols \"1\" and \"0\".\r\n" );
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document.write( "    How many such words do exist, having 7 symbols \"1\" and \r\n" );
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document.write( "        (a)  starting from \"011\" ?\r\n" );
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document.write( "        (b)  ending with \"01\" ?\r\n" );
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document.write( "        (c)  starting from \"011\"  and  ending with \"01\".\r\n" );
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document.write( "     Questions (a), (b) and (c) are three SEPARATE questions.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now everything is clear. See my solution below.\r
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\n" ); document.write( "\n" ); document.write( "Solution\r
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document.write( "(a)  Three leftmost positions are just occupied and, THEREFORE, are not the subject of consideration.\r\n" );
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document.write( "     For the rest 12-3 = 9 positions, we have 7-2 = 5 \"ones\" to distribute.\r\n" );
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document.write( "     We can choose these 5 positions for \"ones\" from 9 positions by    ways.\r\n" );
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document.write( "(b)  Two rightmost positions are just occupied and, THEREFORE, are not the subject of consideration.\r\n" );
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document.write( "     For the rest 12-2 = 10 positions, we have 7-1 = 6 \"ones\" to distribute.\r\n" );
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document.write( "     We can choose these 6 positions for \"ones\" from 10 positions by    =  ways.\r\n" );
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document.write( "(c)  Three leftmost positions and two rightmost positions are just occupied and, THEREFORE, are not the subject of consideration.\r\n" );
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document.write( "     For the rest 12-3-2 = 7 positions, we have 7-2-1 = 4 \"ones\" to distribute.\r\n" );
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document.write( "     We can choose these 4 positions for \"ones\" from 7 positions by    ways.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved. All questions (a), (b) and (c) are answered.\r
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\n" ); document.write( "\n" ); document.write( "Is everything clear to you from my post ?\r
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\n" ); document.write( "\n" ); document.write( "If you still have questions, then let me know.\r
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\n" ); document.write( "\n" ); document.write( "It is how a Math problem should be presented and solved.\r
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\n" ); document.write( "\n" ); document.write( "Crystally clear for EVERYONE.\r
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\n" ); document.write( "\n" ); document.write( "How it was worded and presented in your original post, is good for recycling, only.\r
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\n" ); document.write( "\n" ); document.write( "Probably (I am ready to admit it) it is not your fault, but then it is the fault of the person, who composed this problem . . . \r
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\n" ); document.write( "\n" ); document.write( "Also, for the future, if you have several questions, it is ALWAYS better to separate them and to submit them ONE per POST.\r
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