document.write( "Question 1204282: In how many ways can a committee consisting of 3 men and 7 women be selected from a group consisting of 20 men and 15 women? \n" ); document.write( "
Algebra.Com's Answer #840431 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "n = 20 men
\n" ); document.write( "r = 3 selections
\n" ); document.write( "Order doesn't matter on a committee since none of the seats are labeled (eg: chairman, president, VP, etc), so we use the nCr combination formula.
\n" ); document.write( "n C r = (n!)/(r!(n-r)!)
\n" ); document.write( "20 C 3 = (20!)/(3!*(20-3)!)
\n" ); document.write( "20 C 3 = (20!)/(3!*17!)
\n" ); document.write( "20 C 3 = (20*19*18*17!)/(3!*17!)
\n" ); document.write( "20 C 3 = (20*19*18)/(3!)
\n" ); document.write( "20 C 3 = (20*19*18)/(3*2*1)
\n" ); document.write( "20 C 3 = 6840/6
\n" ); document.write( "20 C 3 = 1140
\n" ); document.write( "There are 1140 ways to select the 3 men from a candidate pool of 20 men.\r
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\n" ); document.write( "\n" ); document.write( "Similar calculations will lead us to 15C7 = 6435 ways to select 7 women from a candidate pool of 15 women.\r
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\n" ); document.write( "\n" ); document.write( "Ultimately there are 1140*6435 = 7,335,900 ways to form this committee.
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