document.write( "Question 1205064: There are 12 members on a board of directors. If they must form a subcommittee of members 3, how many different subcommittees are possible? \n" ); document.write( "

Algebra.Com's Answer #841686 by math_helper(2461) $\"\"$ $\"About$

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document.write( "Assuming the 3 subcommittee members don't have titles (i.e. they serve with equal standing and none are distinguishable from each other with respect to the subcommittee):   
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document.write( "         C(12,3) =  12!/((12-3)!*3!) = 12!/(9!*3!) = 220
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document.write( "Aside...
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document.write( "If there was a \"head of subcommittee\" and \"spokesperson of subcommittee\" then we would not need to divide by the 3! above (similar to \"order matters\") and you'd get:    
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document.write( "          P(12,3) = 12!/(12-3)! = 12!/9! = 1320\r
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document.write( "Aside #2...
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document.write( "If, say, exactly one member was 'spokesperson' and the other two were otherwise equal (without title), you'd have:
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document.write( "             12 * C(11,2) = 12*(11!/(9!*2!)) = 660\r
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document.write( "You can see from the pattern, the more distinctions that are made, the greater the number of subcommittees that can be formed.    \n" );
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