How many quadrilaterals can be formed by joining these points?
For the following two (02) items: There are 8 points on a plane out of which 4 points are collinear.
- A. 70
- B. 69
- C. 53 ✓
- D. None of the above
Correct Answer: C. 53
Explanation
The total number of ways to pick 4 points from 8 is \binom{8}{4} = 70. A quadrilateral cannot be formed if all 4 points are collinear (\binom{4}{4} = 1) or if 3 points are collinear and the 4^{\text{th}} point is chosen from the remaining 4 points (\binom{4}{3} \times \binom{4}{1} = 4 \times 4 = 16). Subtracting these invalid cases, 70 - 1 - 16 = 53 quadrilaterals can be formed.
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