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  4. Given 12 points in a plane, no three of which are collinear. Then number of line segments can be determined, are:

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Q. Given 12 points in a plane, no three of which are collinear. Then number of line segments can be determined, are:

Permutations and Combinations

Solution:

To find number of line segment we will have to draw the line segments joining two points. If n is the number of such lines segments, then
$n =^{12}C_{2} = \frac{12!}{2!\left(12-2\right)!} = \frac{12 \times11 \times10!}{2 \times10!} = 66 $