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

Question

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 (A) 60 (B) 64 (C) 35 (D) 32

Tardigrade Admin · Accepted Answer

Number of ways = (selecting 1 side from 10 sides) × (selecting one vertex out of 6 remaining vertices which are not consecutive to side) = 10 C 1 × 6 C 1=60

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

60

64

35

32

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

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

60

64

35

32

Number of ways = (selecting 1 side from 10 sides) × (selecting one vertex out of 6 remaining vertices which are not consecutive to side) =10C1​×6C1​=60

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