Let Qnbe the number of possible quadrilaterals formed by joining vertices of an n sided regular  polygon. If Qn+1−Qn=20 then value of n is:

Qn= Number of ways of choosing four vertices out of n =nC4∴ 20=Qn+1−Qn=n+1C4−nC4=nC4+nC3−nC4=nC3∵nCr−1+nCr=n+1Cr 16n(n−1)(n−2)=20 ⇒     n3−3n2+2n−120=0⇒     n3−6n2+3n2−18n+20n−120=0⇒     (n−6)n2+3n+20=0    As n∈N,n=6