Good Perm -Combs Formulae & Questions

Perms/Combs Triangles/Circles Concepts:
1. If there are n number of straight lines , They intersect each other in nc2 ways
2. If there are m number of circles , They intersect each other in
2*(mc2) ways = m (m-1)= 2p2 ways
3. When n straight lines and m circles intersect each other , they intersect in
at most 2 * m * n = 2* ( no. of circles ) * ( no.of straight lines)
4. When n parallel lines intersect m straight lines , Then no. of parallelograms possible = nc2 * mc2= mn (m-1) (n-1)/4
5. There is one case when collinear and non- collinear points are given , and asked how many triangles it can formed=>
The funda for this - ( Triangles that can be formed with all points ) – ( Triangles formed with collinear points )
6. To form a Straight line from n no. of points , out of which n1 are collinear and n2 are non – collinear ,
The total no. of straight lines can be formed
=>( Total no. of lines formed with total n points ) – ( total no. of lines that formed with n1 collinear points ) + 1 ( One line can be formed with n1 collinear points)
=> nc2- n1c2 +1
7 .The same is case with circles to be formed with n collinear points and m non- collinear points
=> (m+n)c3- nc3 + 1 ( This 1 circle can be drawn with n collinear points , if points are on circle )
Same is the case with triangles
8 . When there are n points taken on m intersecting lines , intersecting each other at only one point o , then
The possible triangles from these points
( Triangles formed with 0 and n points on one straight line ) * no. of straight lines + ( Triangles formed with total points except 0 ) – ( Triangles formed with n collinear points of m no. of straight lines )
=> Let us modify for n points taken on 2 lines intersecting each other at point 0
=> Thus total no. of points = 2*n+1
=> Point o can formed n triangles with each line = n*n
=> 2nc3-nc3-cn3 + n *n
9 . One standard formula for n no. of straight lines drawn in a plane out of which no. two lines are parallel and no. three lines are concurrent . The number of parts into which these lines divide the plane =
1+ Σ r to n (r)
Let take with 8 straight lines = 1+ 9*8 /2 = 37