document.write( "Question 1037322: a committee of two tutors and five pupils is to be formed among six tutors and ten pupils in how many way can this be done if 1 particular tutor must be on the committee and two particular pupils must not be on the committee \n" ); document.write( "

Algebra.Com's Answer #651994 by Edwin McCravy(20054) $\"\"$ $\"About$

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A committee of two tutors and five pupils is to be formed
\n" ); document.write( "among six tutors and ten pupils in how many way can this
\n" ); document.write( "be done if 1 particular tutor must be on the committee
\n" ); document.write( "and two particular pupils must not BOTH be on the committee.
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document.write( "Since the 1 particular tutor must be on the committee, we \r\n" );
document.write( "place that particular tutor on the committee and then the \r\n" );
document.write( "problem becomes to select only 1 tutor from the 5 remaining \r\n" );
document.write( "tutors and 5 pupils without those two BOTH being on the\r\n" );
document.write( "committee. \r\n" );
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document.write( "First we find the number of committees without regard to\r\n" );
document.write( "whether or not those two pupils are BOTH on the committee.\r\n" );
document.write( "Then we will subtract the number of committees which they \r\n" );
document.write( "are both on.\r\n" );
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document.write( "We can select the remaining tutor \"5 tutors choose 1\"  5C1 ways.\r\n" );
document.write( "We can then select the the 5 pupils \"10 pupils choose 5, \r\n" );
document.write( "or 10C5 ways.\r\n" );
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document.write( "That's (5C1)(10C5)\r\n" );
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document.write( "From that we must subtract the number of committees where those \r\n" );
document.write( "particular pupils are together on the committee:\r\n" );
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document.write( "We can select the remaining tutor \"5 tutors choose 1\"  5C1 ways.\r\n" );
document.write( "We can then select the other 3 pupils besides those 2 in \r\n" );
document.write( "\"8 pupils choose 3: or 8C3 ways. \r\n" );
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document.write( "That's (5C1)(8C3) that we must subtract:\r\n" );
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document.write( "Answer: (5C1)(10C5)-(5C1)(8C3)=(5)(252)-(5)(56)=1260-280=980 ways.\r\n" );
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document.write( "Edwin

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