document.write( "Question 1150832: The Aviation Club at Rocco's school has 12 members (including Rocco). They need to choose a 3 person helicopter committee and a 4 person Glider Committee. Students can serve on either or both committees, but Rocco refuses to serve on both- he will only serve on one or the other. In how many ways can both committees be chosen? \n" ); document.write( "

Algebra.Com's Answer #772342 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "The groups of 3 persons can be formed from 12 persons by   =  =  220 ways (helicopter committee).\r\n" );
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document.write( "The groups of 5 persons can be formed from 12 persons by   =  = 792  ways (Glider committee).\r\n" );
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document.write( "If no other restrictions, then these two committees can be formed by  . = 220*792 = 174240 ways.\r\n" );
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document.write( "From this number, we must subtract the number of 3-member committees and 5-member committees that contain Rocco as one common members.\r\n" );
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document.write( "For 3-member committees, the number of such committees is   =  = 11*5 = 55.\r\n" );
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document.write( "For 5-member committees, the number of such committees is   =  = 330.\r\n" );
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document.write( "Therefore, the ANSWER  to the problem's question is\r\n" );
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document.write( "    . - . = 174240  - 55*330 = 147015 ways.\r\n" );
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