document.write( "Question 1193835: for a bowling team of 4, how many different teams are possible from a group of 10? \n" ); document.write( "
Algebra.Com's Answer #825869 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Assuming that order doesn't matter, we have 10 C 4 = 210 ways to form the team.
\n" ); document.write( "I used the nCr formula as shown in the scratch work below.\r
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\n" ); document.write( "\n" ); document.write( "n C r = (n!)/(r!(n-r)!)
\n" ); document.write( "10 C 4 = (10!)/(4!*(10-4)!)
\n" ); document.write( "10 C 4 = (10!)/(4!*6!)
\n" ); document.write( "10 C 4 = (10*9*8*7*6!)/(4!*6!)
\n" ); document.write( "10 C 4 = (10*9*8*7)/(4!)
\n" ); document.write( "10 C 4 = (10*9*8*7)/(4*3*2*1)
\n" ); document.write( "10 C 4 = (5040)/(24)
\n" ); document.write( "10 C 4 = 210\r
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\n" ); document.write( "\n" ); document.write( "Notice on the third to last step, I have 10*9*8*7 over top 4*3*2*1
\n" ); document.write( "The numerator represents the number of permutations (where order matters) when choosing four people from a pool of ten.
\n" ); document.write( "We divide over 4! = 4*3*2*1 = 24 because this is the number of ways to arrange any group of four people. This leads us to the correct count of 210. This is to avoid overcounting. \r
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\n" ); document.write( "\n" ); document.write( "Answer: 210
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