document.write( "Question 1176008: A certain college has 52 students participating in games.30 play netball, 25 play football , 10 play handball and football ,13 play netball and handball,9 play netball and football while 2 play all the three games. How many students play handball and no other game? \n" ); document.write( "
Algebra.Com's Answer #801873 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "A certain college has 52 students participating in games.30 play netball, 25 play football ,
\n" ); document.write( "10 play handball and football, 13 play netball and handball, 9 play netball and football while 2 play all the three games.
\n" ); document.write( "How many students play handball and no other game?
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document.write( "For 3 subsets N, F and H, apply the inclusive-exclusive formula\r\n" );
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document.write( "    52 = N + F + H - NF - NH - FH + NFH.\r\n" );
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document.write( "Here NF, NH and FH denote in-pair intersections and NFH is the triple intersection.\r\n" );
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document.write( "In this formula, all the terms are given in the condition, except of H.\r\n" );
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document.write( "So we substitute known values and get this equation for H\r\n" );
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document.write( "    52 = 30 + 25 + H - 10 - 13 - 9 + 2,\r\n" );
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document.write( "simplify\r\n" );
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document.write( "    52 = 25 + H\r\n" );
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document.write( "and find \r\n" );
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document.write( "    H = 52 - 25 = 27.\r\n" );
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document.write( "So, 27 play handball.\r\n" );
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document.write( "But we need only those who play handball and no other games.\r\n" );
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document.write( "So, we subtract NH= 13 and FH= 10  from  H= 27  and add  NFH= 2\r\n" );
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document.write( "       \"H%5Bonly%5D\" = 27 - 13 - 10 + 2 =   6.    ANSWER\r\n" );
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document.write( "ANSWER.  6 students play handball only.\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this forum, this woman just proved it MANY TIMES that she is incompetent in Combinatorics.\r
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