document.write( "Question 1025984: if a given set has nine elements, how many of its subsets have at least five elements? \n" ); document.write( "

Algebra.Com's Answer #641304 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "if a given set has nine elements, how many of its subsets have at least five elements?
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document.write( " = \r\n" );
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document.write( "= 1 + 9 + 36 + 84 + 126 + 126 = 382,\r\n" );
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document.write( "where  is the number of combinations of n things taken k at a time.\r\n" );
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document.write( "There is  = 1 empty subset.\r\n" );
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document.write( "There are  = 9 subsets consisting of 1 element.\r\n" );
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document.write( "There are  = 36 subsets consisting of 2 elements.\r\n" );
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document.write( "There are  = 84 subsets consisting of 3 elements.\r\n" );
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document.write( "There are  = 126 subsets consisting of 4 elements.\r\n" );
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document.write( "There are  = 126 subsets consisting of 5 elements.\r\n" );
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document.write( "Regarding combinations, see the lesson Introduction to Combinations in this site.\r\n" );
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document.write( "Answer. 382 subsets, including one empty subset.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice.\r
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\n" ); document.write( "\n" ); document.write( "Dear Mr. Edwin McCravy,\r
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\n" ); document.write( "\n" ); document.write( "in your post you publicly said that my solution is incorrect.\r
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\n" ); document.write( "\n" ); document.write( "But is IS correct due to obvious reasons.\r
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\n" ); document.write( "\n" ); document.write( "So I ask you to make a public acknowledgment in your post,
\n" ); document.write( "that you take your words back and recognize that you were wrong and my solution is correct.\r
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\n" ); document.write( "\n" ); document.write( "It doesn't require much time to get the right conclusion.
\n" ); document.write( "Finally, it is important for the student to know the truth.\r
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\n" ); document.write( "\n" ); document.write( "If it is difficult to you to make such contr-statement,
\n" ); document.write( "you can simply change your post correspondingly.\r
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\n" ); document.write( "\n" ); document.write( "When I see it, I will take off this notice from my post.\r
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\n" ); document.write( "\n" ); document.write( "Thank you.\r
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