document.write( "Question 870213: Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways this be done if one particular physicist must be on the committee? \n" ); document.write( "
Algebra.Com's Answer #524725 by jim_thompson5910(35256)\"\" \"About 
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If one particular physicist must be on the committee, then you really only have 3-1=2 slots left for physicists. So you'll have 7-1 = 6 physicists left to pick from.\r
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\n" ); document.write( "\n" ); document.write( "There are 5 nCr 2 = 10 ways to pick 2 mathematicians (from a pool of 5)\r
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\n" ); document.write( "\n" ); document.write( "There are 6 nCr 2 = 15 ways to pick 2 physicists (from a pool of 6)\r
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\n" ); document.write( "\n" ); document.write( "Side Note: I'm using the combination formula to compute nCr\r
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\n" ); document.write( "\n" ); document.write( "So there are 10*15 = 150 ways to form a 4 person committee (2 mathematicians and 2 physicists)\r
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\n" ); document.write( "\n" ); document.write( "By extension, there are also 150 ways to form a 5 person committee (2 mathematicians and 3 physicists) with one physicist slot taken. This is because that particular physicist who must be on the committee doesn't change the count (you'll have 1*150 = 150) \n" ); document.write( "
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