First slide

Combinations

Question

Two straight lines intersect at a point O. Points A₁, A₂, …, A_n are taken on one line and points B₁, B₂, …, B_n on the other. If the point O is not to be used, the number of triangles that can be drawn using these points as vertices, is

Moderate

A

n (n – 1)
B

n (n – 1)²
C

n² (n – 1)
D

n² (n – 1)²

Solution

No. of triangles $= n_{C_{1}} .^{n} C_{2} + n_{C_{1}} .^{n} C_{2}$
$\begin{array}{ll} = 2 n . \frac{n (n - 1)}{2} = n^{2} (n - 1) \end{array}$

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