We need maximum no of component so we have to find a connected component which cover all the edges with as minimum vertices possible. Now this can be possible if the connected component is a complete graph which contains maximum number of edges and the remaining vertices will create distinct connected component with no edges.
So, Now say the component which cover the edges say have n vertices,
So number of edges =$\frac{n*(n-1)}{2}$
$\frac{n*(n-1)}{2}= 15$
$n = 6$
So, We have a component of 6 vertices which cover all the edges and rest 9 vertices have no edges creating 9 isolated connected component.
so we have total 10 maximum number of connected components possible.