Question 491951: There are 12 points P1, P2, ..., P12 in the plane, no three of them on the same line.
(a) How many triangles can be formed?
(b) How many of the triangles contain the point P1 as a vertex?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! There are 12 points P1, P2, ..., P12 in the plane, no three of them on the same line.
(a) How many triangles can be formed?
A triangle is determined by 3 non-collinear points.
Ans: 12C3 = (12*11*10)/(1*2*3) = 220 triangles
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(b) How many of the triangles contain the point P1 as a vertex?
One way to pick P1
11C2 ways to pick the other two vertices
Ans: 1*(11*10)/(1*2) = 55 triangles with P1 as a vertex
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Cheers,
Stan H.
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