There are ten point in plane of these ten points four points are in straight line and with exception of these four points ,no other three are in same straight line .Find the number of triangles formed?
2006-12-26 06:54:35 · 4 answers · asked by miinii 3 in Science & Mathematics ➔ Mathematics
116. Label the 4 collinear points set A, the other 6 set B. There are three cases:
1) all three points are in set B. This can happen 6C3, or 20, different ways.
2) one point is in set A. This can happen 4C1*6C2 = 60 different ways.
3) two points are in set A. This can happen 4C2*6C1 = 36 different ways.
So there are 20+60+36=116 different triangles.
Note that a triangle is simply a set of three non-collinear points.
If the ten points were all non-collinear, then we could form 10C3 = 120 triangles. However, we must ignore the 4C3 = 4 triangles formed from 3 points in set A, since they are collinear. So, again, we have 120-4=116.
Steve
2006-12-26 07:03:58 · answer #1 · answered by Anonymous · 0⤊ 0⤋
30
2006-12-26 15:01:57 · answer #2 · answered by whatchalookinat 1 · 0⤊ 1⤋
42
2006-12-26 15:01:38 · answer #3 · answered by pechorin1 3 · 0⤊ 1⤋
116 triangle
2006-12-26 15:52:03 · answer #4 · answered by imamulleith 2 · 0⤊ 0⤋