document.write( "Question 1104312: Use the formula nCr for to evaluate the expression.\r
\n" ); document.write( "\n" ); document.write( "9C1 \n" ); document.write( "
Algebra.Com's Answer #719062 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "The n C r formula is
\n" ); document.write( "n C r = (n!)/(r!(n-r)!)\r
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\n" ); document.write( "\n" ); document.write( "The exclaimation marks mean factorial. Writing something like 6! means we start at 6 and count our way down to 1. Throughout the countdown, we multiply out the terms
\n" ); document.write( "6! = 6*5*4*3*2*1\r
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\n" ); document.write( "\n" ); document.write( "So we'll be using
\n" ); document.write( "9! = 9*8*7*6*5*4*3*2*1
\n" ); document.write( "8! = 8*7*6*5*4*3*2*1
\n" ); document.write( "and
\n" ); document.write( "1! = 1\r
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\n" ); document.write( "\n" ); document.write( "Meaning that
\n" ); document.write( "n C r = (n!)/(r!(n-r)!)
\n" ); document.write( "9 C 1 = (9!)/(1!*(9-1)!)
\n" ); document.write( "9 C 1 = (9!)/(1!*8!)
\n" ); document.write( "9 C 1 = (9*8*7*6*5*4*3*2*1)/((1)*(8*7*6*5*4*3*2*1))
\n" ); document.write( "9 C 1 = (362880)/((1)*(40320))
\n" ); document.write( "9 C 1 = (362880)/(40320)
\n" ); document.write( "9 C 1 = 9\r
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\n" ); document.write( "\n" ); document.write( "As a shortcut,
\n" ); document.write( "n C r = (n!)/(r!(n-r)!)
\n" ); document.write( "9 C 1 = (9!)/(1!*(9-1)!)
\n" ); document.write( "9 C 1 = (9!)/(1!*8!)
\n" ); document.write( "9 C 1 = (9*8!)/(1!*8!)
\n" ); document.write( "9 C 1 = 9/1
\n" ); document.write( "9 C 1 = 9
\n" ); document.write( "which works because the 8! is buried inside of 9!, allowing us to say 9! = 9*8!
\n" ); document.write( "So the \"8!\" terms cancel out\r
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\n" ); document.write( "\n" ); document.write( "Answer: 9
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