Aptitude Discussion

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

✖ A. |
495 |

✖ B. |
550 |

✔ C. |
1045 |

✖ D. |
2475 |

**Solution:**

Option(**C**) is correct

We can get the triangles in two different ways.

Taking two points from the line having 10 points

(in \(^{10}C_2\) ways, i.e., 45 ways) and one point from the line consisting of 11 points (in 11 ways).

So, the number of triangles here is $45 \times 11 = 495$.

Taking two points from the line having 11 points (in \(^{11}C_2\), i.e., 55 ways) and one point from the line consisting of 10 points (in 10 ways), the number of triangles here is $55 \times 10 = 550$

Total number of triangles,

$= 495 + 550$

$= \textbf{1,045 triangles}$