How to randomly get or find a sub-tree (include root node) from a given tree that contains n nodes

I have a non-binary tree. I want to randomly find a "sub-trees" that are connected to root which must have at least n nodes. For example: given a tree as below

            A
          /   \
         B     C
        / \     \
       E   D     F
            \
             J

n = 4

A random sub-tree that contains 4 nodes could be:

            A
          /   
         B    
          \   
           D  
            \
             J

or

            A
          /   \
         B     C
                \
                 F

I don't need to get all possible sub-trees, just randomly get it with a given tree and n