In a plane,there are 37 straight lines,of whi | vedclass

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Question

(C) The total number of ways to select $2$ lines out of $37$ is $^{37}C_2$. Since $13$ lines are concurrent at point $A$,they do not produce $^{13}C_2

Vedclass · Accepted Answer

$^{37}C_2 - ^{13}C_2 - ^{11}C_2 + 2$

Vedclass · Answer

(C) The total number of ways to select $2$ lines out of $37$ is $^{37}C_2$. Since $13$ lines are concurrent at point $A$,they do not produce $^{13}C_2$ distinct intersection points; instead,they all intersect at $1$ point. Thus,we subtract $^{13}C_2$ and add $1$. Similarly,since $11$ lines are concurrent at point $B$,they do not produce $^{11}C_2$ distinct intersection points; they all intersect at $1$ point. Thus,we subtract $^{11}C_2$ and add $1$. Therefore,the total number of points of intersection is $^{37}C_2 - ^{13}C_2 + 1 - ^{11}C_2 + 1 = ^{37}C_2 - ^{13}C_2 - ^{11}C_2 + 2$.

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