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  4. Number of triangles that can be made using vertices of a polygon of 10 sides as their vertices and having exactly one side common with the polygon is

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Q. Number of triangles that can be made using vertices of a polygon of 10 sides as their vertices and having exactly one side common with the polygon is

Permutations and Combinations

Solution:

Number of ways = (selecting 1 side from 10 sides) $\times$ (selecting one vertex out of 6 remaining vertices which are not consecutive to side)
$={ }^{10} C _1 \times{ }^6 C _1=60$