Number of points of intersection of n straight lines if n satisfies  n+5Pn+1=11(n−1)2×n+3Pn is

n+5Pn+1=11(n−1)2×n+3Pnor  n+5Pn+1=(n+5)!4!=11(n−1)2(n+3)!3!or (n+5)(n+4)=22(n−1)After solving, we get n = 6 or n = 7.The number of points of intersection of lines is  6C2 or  7C2≡15 or 21.