| The total number of triangles that can be formed from 12 points out of which 4 points arc collinear, is |
A) 220
B) 224
C) 216
D) 210
Correct Answer: C
Solution :
| Total number of triangles which can be formed by selecting any three points from 12 points \[={}^{12}{{C}_{3}}\] |
| Since, 4 points are collinear. |
| Selecting three points from these 4 points \[={}^{4}{{C}_{3}}\] |
| So, required number of triangles which can be formed |
| \[={}^{12}{{C}_{3}}-{}^{4}{{C}_{3}}\] |
| \[=\frac{12\times 11\times 10}{3\times 2\times 1}-\frac{4\times 3\times 2}{3\times 2\times 1}\] |
| \[=220-4=216\] |
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