Combinatorics: Triangles from Points

CAT 1999 Slot 1 · QA · Easy · Permutations and Combinations

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Ten points are marked on a straight line and 11 points are marked on another parallel straight line. How many triangles can be constructed with vertices from among the above points?

  1. A.

    495

  2. B.

    550

  3. C.

    1045

  4. D.

    2475

Answer

C

Explanation

A triangle requires 3 vertices. We can either choose 2 points from line 1 and 1 from line 2, or 1 point from line 1 and 2 from line 2: Number of triangles = (102)×11+10×(112)=45×11+10×55=495+550=1045\binom{10}{2} \times 11 + 10 \times \binom{11}{2} = 45 \times 11 + 10 \times 55 = 495 + 550 = 1045.

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