Question

Out of 10 non- collinear points, how many pentagons can be made?​

Answer 1

Answer:

This  can  be  found  out  by  Combination formula .

(10)C(2) = 10!/(2!)(8!)

             = 10 * 9/2

             = 5 * 9

             = 45

∴  Pentagons  can  be  made  in  45  ways  by  10  non-collinear points .

Step-by-step explanation:

Answer 2

Answer:

Since no three points are collinear in the plane ,a triangle can be formed by selecting any three point.

So total number of triangles = number of ways of selecting 3 points from the given set of points

Therefore total number of triangles = 10c3 =(10)!/(3!*7!) = (10*9*8)/(3*2*1) = 10*3*4 =120

Hope it helps !!!