When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? _____________ , When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? _____________

Solution

D. 6

Explanation

 

Consider a point O inside the tetrahedron as in fig below and connect it with any two of its corners (suppose A and B), we will get 1 internal plane OAB. Similarly, we can get OAC, OAD, OBC, OBD, OCD i.e. No. of internal planes is 6.

or 

calculation is also  the possible corners by using combinations formula,
which is nCr, i.e. no of ways to select a combination of r things from a given set of n things.
here n = 4 ( as total 4 vertices, A,B,C and D)
and r =2 ( as we need two corners at a time)
Thus, 4C2 = 6.