Question

Number of quadrilaterals that can be constructed from the vertices of a decagon (10 sided polygon) such that none of the sides of the quadrilateral is also a side of the decagon, is –

• A. 25
• B. 50
• C. 100
• D. 200

Answer 1

Answer: (A)

25

Answer 2

First vertex can be selected in ¹⁰C₁ ways.

First vertex

Now, two neighbouring vertices are not to be selected.

Among the remaining 7 vertices 3 are to be selected and 4 are not to be selected.

Now mark the 4 vertices not to be selected by × sign and then these can be partitioned by 5 partitions from these partitions we are to select 3. This can be done in ⁵C₃ ways and these are the places where the remaining 3 vertices can be chosen.

\ number of ways = $\frac{10C_{1} \times^{5}C_{3}}{4}$= 25