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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.

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