document.write( "Question 1203152: A committee of 5 people is to be chosen from 6 midfielders, 3 attackers and 7 referees. If each discipline must be represented, determine the number of ways of selecting the committee to include: (a) exactly one midfielder and one attacker. (b) exactly two midfielders; (c) at least two midfielders. \n" ); document.write( "

Algebra.Com's Answer #838485 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A committee of 5 people is to be chosen from 6 midfielders, 3 attackers and 7 referees.
\n" ); document.write( "If each discipline must be represented, determine the number of ways of selecting
\n" ); document.write( "the committee to include:
\n" ); document.write( "(a) exactly one midfielder and one attacker.
\n" ); document.write( "(b) exactly two midfielders;
\n" ); document.write( "(c) at least two midfielders.
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\n" ); document.write( "\n" ); document.write( " I will answer (a) and (b), leaving (c) for your own solution/exercise.\r
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document.write( "(a)  In this case, the committee is 1 midfielder, 1 attacker and 5-1-1 = 3 referees.\r\n" );
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document.write( "     THEREFORE, the number of possible committees is   = 6*3*35 = 630.   ANSWER\r\n" );
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document.write( "(b)  In this case, the committee is 2 midfielders and 3 persons from ((6+3+7)-2) = 14 other people.\r\n" );
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document.write( "     THEREFORE, the number of possible committees is   = 15*364 = 5460.   ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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