Question

Number of points of intersection of $n$ straight lines if $n$ satisfies ${}^{n+5}{P}_{n+1}=\frac{11(n-1)}{2}\times {}^{n+3}{P}_n$ is

• A. 15
• B. 28
• C. 21
• D. 10

Answer 1

Answer: (A), (C)

${}^{n+5}{P}_{n+1}=\frac{11(n-1)}{2}\times {}^{n+3}{P}_n$
or ${}^{n+5}{P}_{n+1}=\frac{(n+5)!}{4!}=\frac{11(n-1)}{2}\frac{(n+3)!}{3!}$
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
${}^6{C}_2$ or ${}^7{C}_2\equiv 15$ or $21$.