Thanks ArchedScythe,
I have learned from you.
I just want to write your logic using different words. (note : for this question rotations are NOT the same)
There are 7 points on the circle.
Every chord must join 2 points so there there is a total of 7C2=21 possible chords
So
the number of ways to choose ANY 4 chords is 21C4 = 5985
That is the sample space.
NOW
To make a bow tie we must choose 4 points.
There are 7C4 = 35 ways to chose four points.
Now how many ways are there to join these 4 points into a bow tie using just 4 chords.
If you draw it on a peice of paper you will see that there are only 2 ways.
So
There are 70 ways a bow tie can be created.
P( the 4 chords create a bowtie) = 70 / 5985
Just like ArchedScythe said.