First of all , we should know that in set theory the order does not matter and hence the same for subsets as well .e.g. If {1,2) is a subset of some set then {2,1} is all the same and hence this need not be counted again.
So this is a problem of combination rather than permutation.
Therefore ,
No of vertices = No of 3 element subsets of 10 element set
= No of ways of selection of 3 objects out of 10 objects
= 10C3
= 120
So no of vertices = 120 ................(1)
Now the edge is drawn only if the subsets are disjoint.Now we have to do systematically for this :
Consider a subset {1,2,3} of the set {1,2,........,10} which is hence a vertex as well.Now for disjointedness , we can select anything from the given set except 1 , 2 , 3
So no of remaining elements = 7
So degree of vertex {1,2,3} = No of edges that are incident on {1,2,3} (or) no of vertices which are adjacent to {1,2,3}
= No of disjoint subsets w.r.t {1,2,3}
= 7C3 [ as we have remaining elements of set = 7 and any 3 of them together constitutes a vertex.Also order does not matter as mentioned earlier]
= 35
So sum of degree = No of vertices * Degree of each vertex [As here degree of a vertex is going to be same]
= 120 * 35
= 4200
So no of edges using the theorem :
Sum of degree = 2 * No of edges
(or) No of edges = 4200 / 2
(or) No of edges = 2100
Hence B) should be the correct option.