Discussion

Question:

P . . . . . Q
R . . . . . S
T . . . . . U
V . . . . . W

Using 5 dots in each of the lines PQ, RS, TU and VW as the vertices, how many triangles can be drawn such that the base is on any one of the above lines?

Explanation:

The base has to be on one of the four lines.

Hence, the base can first be chosen in 4 ways.

Now, on this base, two points need to chosen from five to form the actual base. This can be done in ⁵C₂ ways i.e. 10 ways

For the third point, one of three lines has to be chosen and then one of five points from each line has to be chosen.

∴ Number of possible triangles = 4 × 10 × 3 × 5 = 600

Hence, option (d).

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