Solve this for me please!!

We have $37 \choose 2$ ways to choose a pair of lines from the 37 points. Each pair will determine a unique intersection point except among those 13 points passed through point $A$ and among those 11 points passed through point $B$ . Hence, the number of intersection points is ${37 \choose 2} - {13 \choose 2} + 1 - {11 \choose 2} + 1 = 535$ .

Let each line that passes through point A be known as an 'A' line. Let each line that passes through point B be known as a 'B' line. Let each line that passes through neither point A nor point B be known as an 'K' line.

Since there 13 A lines, 11 B lines, and a total of 37 lines, the number of K lines = 37-13-11 = 13.

Case 1: An A line intersects with a B line Number of options for the A line = 13. Number of options for the B line = 11. To combine these options, we multiply: 13*11 = 143.

Case 2: An N line intersects with an A or B line Number options for the N line = 13. Number of options for the A or B line = 13+11 = 24. To combine these options, we multiply: 13*24 = 312.

Case 3: An N line intersects with another N line Each PAIR of N lines will yield an intersection. From the 13 N lines, the number of ways to choose 2 = 13C2 = (13 * 12) / ( 2 * 1 ) = 78.

Case 4: Points A and B Points A and B constitute 2 more intersections.

Total intersections = 143+312+78+2 = 535.

A = 13.12÷2=78 pairs of lines B = 11.10÷2=55 pairs of lines

Number of intersactions=37.36÷2=666 But we are counting 78 times the point A and 55 times the point B

So: 666 - 78 - 55= 533

But now we don't count A and B

Finally : 533 + 2 = 535