There are 7 non-collinear points. How many triangles can be drawn by joining these points?
A. 35
B. 10
C. 8
D. 7
Answer: Option A
Solution(By Examveda Team)
A triangle is formed by joining any three non-collinear points in pairs. There are 7 non-collinear points. The number of triangles formed, $$\eqalign{ & { = ^7}{{\text{C}}_3} \cr & = \frac{{7 \times \left( {7 - 1} \right) \times \left( {7 - 2} \right)}}{{3!}} \cr & = \frac{{7 \times 6 \times 5}}{{3 \times 2 \times 1}} \cr & = 7 \times 5 \cr & = 35 \cr} $$Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
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