document.write( "Question 1104421: GIVEN 4 noncoplanar points, no three of which are collinear. How many planes are determined by the 4 points? Thanks! \n" ); document.write( "
Algebra.Com's Answer #719151 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "Rule: Three noncollinear points are needed to uniquely define a plane\r
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\n" ); document.write( "\n" ); document.write( "Call the points A, B, C and D. There are exactly four ways to pick three points from this list where order doesn't matter. Put another way, there are 4 ways to exclude a point that isn't going to be determining a plane\r
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\n" ); document.write( "\n" ); document.write( "Those four ways are:
\n" ); document.write( "{B, C, D} ... notice we leave out A
\n" ); document.write( "{A, C, D} ... notice we leave out B
\n" ); document.write( "{A, B, D} ... notice we leave out C
\n" ); document.write( "{A, B, C} ... notice we leave out D\r
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\n" ); document.write( "\n" ); document.write( "Alternatively, you can use the n C r formula to get the same result. Use n = 4 and r = 3
\n" ); document.write( "n C r = (n!)/(r!(n-r)!)
\n" ); document.write( "4 C 3 = (4!)/(3!*(4-3)!)
\n" ); document.write( "4 C 3 = (4!)/(3!*1!)
\n" ); document.write( "4 C 3 = (4*3!)/(3!*1!)
\n" ); document.write( "4 C 3 = (4)/(1!)
\n" ); document.write( "4 C 3 = (4)/(1)
\n" ); document.write( "4 C 3 = 4\r
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\n" ); document.write( "\n" ); document.write( "Answer: 4 planes
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