SOLUTION: GIVEN 4 noncoplanar points, no three of which are collinear. How many planes are determined by the 4 points? Thanks!

Question 1104421: GIVEN 4 noncoplanar points, no three of which are collinear. How many planes are determined by the 4 points? Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Rule: Three noncollinear points are needed to uniquely define a plane

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

Those four ways are:
{B, C, D} ... notice we leave out A
{A, C, D} ... notice we leave out B
{A, B, D} ... notice we leave out C
{A, B, C} ... notice we leave out D

Alternatively, you can use the n C r formula to get the same result. Use n = 4 and r = 3
n C r = (n!)/(r!(n-r)!)
4 C 3 = (4!)/(3!*(4-3)!)
4 C 3 = (4!)/(3!*1!)
4 C 3 = (4*3!)/(3!*1!)
4 C 3 = (4)/(1!)
4 C 3 = (4)/(1)
4 C 3 = 4

Answer: 4 planes

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