document.write( "Question 830897: From 6 teachers and 4 students. a committee of 6 is to be formed. In how many ways can this be done if the committee contains (1) exactly 2 teachers (2) at least 2 students. \n" ); document.write( "
Algebra.Com's Answer #501062 by Edwin McCravy(20055)\"\" \"About 
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document.write( "(1) exactly 2 teachers\r\n" );
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document.write( "   Choose the 2 teachers in C(6,2) ways.  That's 15 ways.\r\n" );
document.write( "   Choose the 4 students in C(4,4) ways.  That's 1 way.\r\n" );
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document.write( "   Answer: 15*1 = 15\r\n" );
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document.write( "(2) at least 2 students.\r\n" );
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document.write( "  First find the number of committees consisting of any 6 of the 10 people\r\n" );
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document.write( "  Choose any 6 from the 10 people in C(10,6) ways.  That's 210 ways.   \r\n" );
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document.write( "  Then subtract the following from that number\r\n" );
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document.write( "       a. The number of committees with 1 student and 5 teachers\r\n" );
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document.write( "          Choose 1 student in C(4,1) ways.  That's 4 ways\r\n" );
document.write( "          Choose 5 teachers in C(6,5) ways.  That's 6 ways\r\n" );
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document.write( "          That's 4*6 = 24 ways  \r\n" );
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document.write( "       b. The committee with 0 students and 6 teachers.\r\n" );
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document.write( "          Choose all 6 teachers.  That's C(6,6) or 1 way\r\n" );
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document.write( "Answer: 210 - 24 - 1 = 185 ways.\r\n" );
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document.write( "Edwin

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