Question

Find the number of quadrilateral which can be constructed by joining the vertices of a convex polygon of 20 sides, if none of the side of the polygon is also the side of the quadrilateral

Answer 1

Answer: 2275

We have number of quadrilateral
$={}^{17}{C}_4-{}^{15}{C}_2=\frac{17\cdot 16\cdot 15\cdot 14}{1\cdot 2\cdot 3\cdot 4}-\frac{15\cdot 14}{1\cdot 2}=(10)(17)(14)-(15)(7)$
$=2380-105=2275$
Alternatively :
$\text{ Number of quadrilateral fromed }=\frac{{}^{20}{C}_1\times {}^{15}{C}_3}{4}=25\times 91=2275$